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ArtStudies/M2/Reinforcement Learning/Lab 4 - Monte Carlo Control in Blackjack game.ipynb
Arthur DANJOU 3e1ac18acd Add Lab 4
2026-01-13 10:36:09 +01:00

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{
"cells": [
{
"cell_type": "markdown",
"id": "2846680b-b04d-41ab-8891-85b6db569a29",
"metadata": {},
"source": [
"# Lab 4 - Monte Carlo Control in Blackjack game\n",
"\n",
"## 1. Objectives\n",
"\n",
"In this lab, we will:\n",
"\n",
"1. Understand how Monte Carlo methods can be used to estimate value functions from experience, without knowing the transition probabilities of the environment.\n",
"\n",
"2. Model the Blackjack game as an episodic Markov Decision Process (MDP) with terminal rewards.\n",
"\n",
"3. Implement first-visit Monte Carlo policy evaluation to estimate state-value and action-value functions.\n",
"\n",
"4. Apply Monte Carlo control to learn an optimal policy for Blackjack.\n",
"\n",
"5. Address the exploration problem by using exploring starts and $\\varepsilon$-soft policies.\n",
"\n",
"6. Study off-policy Monte Carlo learning and understand how a target policy can be evaluated using data generated by a different behavior policy. Implement importance sampling (ordinary and weighted) to correct the distribution mismatch in off-policy learning.\n",
"\n",
"-------------------"
]
},
{
"cell_type": "markdown",
"id": "3c9bbf3c-3974-4996-b1c9-805dd9935905",
"metadata": {},
"source": [
"## 2. Blackjack game\n",
"\n",
"Blackjack is a card game played between a **player** and a **dealer**. The goal is to obtain a hand value as close as possible to 21, without exceeding it.\n",
"\n",
"- Card values\n",
" - Number cards (2–10): face value\n",
" - Face cards (J, Q, K): value 10\n",
" - Ace (A): value 1 or 11\n",
" - The Ace (A) is a special card in Blackjack because it can take two possible values: 1 or 11.\n",
" - When an Ace is counted as 11 without making the hand exceed 21, we say the hand has a usable ace.\n",
" - If counting the Ace as 11 would cause the total to exceed 21, the Ace is automatically counted as 1.\n",
" - This choice is not an action taken by the player; it is an automatic rule of the game that always favors avoiding a bust.\n",
"\n",
"\n",
"- Game flow\n",
" - The game starts by giving the player an initial hand and showing one visible card for the dealer.\n",
" - The player then plays first and repeatedly chooses between:\n",
" - **Hit**: draw one additional card\n",
" - **Stick**: stop drawing cards\n",
" - If the player’s total exceeds 21 at any time, the episode ends immediately with a loss.\n",
" - After the player sticks, the dealer plays:\n",
" - The dealer must hit until the hand value is at least 17\n",
" - Then the dealer sticks\n",
"\n",
"- Outcome and rewards\n",
" - Player wins if their final hand value is higher than the dealer’s without busting.\n",
" - Player loses if they bust or if the dealer has a higher hand.\n",
" - A draw (tie) gives zero reward.\n",
"\n",
"**Next, we will model the Blackjack game as an episodic Markov Decision Process (MDP) with terminal rewards.**"
]
},
{
"cell_type": "markdown",
"id": "52633063-0087-4290-9b04-ed23dd8ab04d",
"metadata": {},
"source": [
"### 2.0 Imports and global settings"
]
},
{
"cell_type": "code",
"execution_count": 218,
"id": "ae5c04c2-e544-4307-a82e-63d920383bb5",
"metadata": {},
"outputs": [],
"source": [
"from collections import defaultdict\n",
"\n",
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"\n",
"# Reproducibility\n",
"rng = np.random.default_rng(0)"
]
},
{
"cell_type": "markdown",
"id": "d3bca55f-6db6-4400-9b8f-c21cfb0c14e5",
"metadata": {},
"source": [
"### 2.1 Blackjack environment (State, Action, Episode, Rewards)\n",
"\n",
"1. State is a summary of the game \n",
"$$\n",
"s=(p,d,u)\n",
"$$\n",
"where\n",
" - $p =$ player's current sum \n",
" - $d =$ dealer’s showing card (1–10)\n",
" - $u =$ usable ace indicator (0/1)\n",
"\n",
" \n",
"2. Player's action :\n",
" - STICK = 0\n",
" - HIT = 1\n",
" \n",
"3. Episode ends when:\n",
" - player busts (sum > 21), or\n",
" - player sticks and dealer finishes their fixed policy (hit until 17)\n",
"\n",
"4. Rewards:\n",
" - player bust: −1\n",
" - else at terminal after dealer plays: win +1, lose −1, draw 0\n",
" - Here, intermediate rewards are 0; only terminal reward matters. \n",
"\n",
"5. Uniform card draws: Here in this lab, we assume a uniform draw of cards to simplify the environment and preserve the Markov property.\n",
" - With uniform draws: future cards are independent of the past; the state $(p,d,u)$ is sufficient.\n",
" - With a real deck: card probabilities depend on the history of drawn cards; therefore, the state $(p,d,u)$ is no longer Markov."
]
},
{
"cell_type": "code",
"execution_count": 219,
"id": "5b5110be-3795-495b-aacc-67b6d4798109",
"metadata": {},
"outputs": [],
"source": [
"# In Blackjack the player has two possible decisions:\n",
"STICK = 0 # STICK: stop drawing cards (end the player's turn)\n",
"HIT = 1 # HIT: draw one more card\n",
"ACTIONS = [STICK, HIT] # the list of all valid actions"
]
},
{
"cell_type": "markdown",
"id": "bd019f08-fb38-4086-aac6-5cbead812007",
"metadata": {},
"source": [
"We now define a function that draws a card with a value in $\\{1,2,\\cdots,10\\}$.\n",
" \n",
"1. The value 1 represents an Ace.\n",
"2. The value 10 represents any 10, Jack, Queen, or King, all of which are treated as having value 10.\n",
"\n",
"**Important** To simplify the environment and make it suitable for modeling as a Markov Decision Process (MDP), we assume that cards are drawn uniformly from this set. This removes the need to track the remaining deck composition and allows the transition dynamics to depend only on the current state."
]
},
{
"cell_type": "code",
"execution_count": 220,
"id": "006775e4-940d-4cc2-a6d7-bd0481609f4f",
"metadata": {},
"outputs": [],
"source": [
"def draw_card(rng: np.random.Generator) -> int:\n",
" \"\"\"Draw a card value in {1,...,10}. Face cards have value 10.\"\"\"\n",
" return int(rng.integers(1, 11))\n"
]
},
{
"cell_type": "markdown",
"id": "6e2740fd-5be3-49c8-827d-d75d35aa441f",
"metadata": {},
"source": [
"Now we define a function `usable_ace(hand)` to detect whether an Ace in hand can be trated as “11”, which means, it is a usable ace.\n",
"\n",
"Recall that a “usable ace” means: the hand contains an Ace (1 in hand) and we can treat that Ace as 11 instead of 1 without going over 21. \n",
"\n",
"Examples:\n",
"- hand = [1, 7] $\\rightarrow$ sum(hand)=8 $\\rightarrow$ 8+10=18 <= 21 $\\rightarrow$ usable ace = True\n",
"- hand = [1, 7, 5] $\\rightarrow$ sum=13 $\\rightarrow$ 13+10=23 > 21 $\\rightarrow$ usable ace = False (Here ace must be counted as 1)\n"
]
},
{
"cell_type": "code",
"execution_count": 221,
"id": "76573eb5-73a7-4250-908c-682e17ac9a67",
"metadata": {},
"outputs": [],
"source": [
"def usable_ace(hand: list[int]) -> bool:\n",
" \"\"\"Return True if hand has an ace (value 1) that can be counted as 11 without busting.\"\"\"\n",
" return (1 in hand) and (sum(hand) + 10 <= 21) # noqa: PLR2004\n"
]
},
{
"cell_type": "markdown",
"id": "2d4ae74e-3b11-4c8b-8b28-86deab846830",
"metadata": {},
"source": [
"This `sum_hand(hand)` function returns the hand’s effective score under Blackjack rules:\n",
"\n",
"1. If there is a usable ace, count one ace as 11 (add 10).\n",
"2. Otherwise, just return the raw sum.\n",
"\n",
"Why “best” sum? Since Blackjack players always prefer the highest total $\\leq$ 21.\n"
]
},
{
"cell_type": "code",
"execution_count": 222,
"id": "e520924e-dd82-45ff-b039-fde966da7a65",
"metadata": {},
"outputs": [],
"source": [
"def sum_hand(hand: list[int]) -> int:\n",
" \"\"\"Return best (highest) sum <=21 if possible by counting usable ace as 11. Otherwise return the raw sum.\"\"\"\n",
" s = sum(hand)\n",
" if usable_ace(hand):\n",
" return s + 10\n",
" return s"
]
},
{
"cell_type": "markdown",
"id": "3d8b22e4-c828-4a2b-8228-d34bfbe36e0c",
"metadata": {},
"source": [
"Now we define `is_bust(hand)` function to check if we exceed 21. "
]
},
{
"cell_type": "code",
"execution_count": 223,
"id": "83fa2134-a552-4a83-991a-ae8dd46eb139",
"metadata": {},
"outputs": [],
"source": [
"def is_bust(hand: list[int]) -> bool:\n",
" \"\"\"Return True if hand sum exceeds 21.\"\"\"\n",
" return sum_hand(hand) > 21 # noqa: PLR2004\n"
]
},
{
"cell_type": "markdown",
"id": "4d78d770-a3fb-445e-906d-ca5dc0f78861",
"metadata": {},
"source": [
"Now we define `score(hand)` for the terminal “value” of a hand. It returns a “hand score” used at the end of a game:\n",
"\n",
"1. If bust: score = 0 (player is effectively dead)\n",
"2. Else: score = effective sum"
]
},
{
"cell_type": "code",
"execution_count": 224,
"id": "7ab1c557-d03b-45e3-b821-6d7eb3879f67",
"metadata": {},
"outputs": [],
"source": [
"def score(hand: list[int]) -> int:\n",
" \"\"\"Terminal score is 0 if bust otherwise sum_hand.\"\"\"\n",
" return 0 if is_bust(hand) else sum_hand(hand)"
]
},
{
"cell_type": "markdown",
"id": "b3d443e6-3f15-4c6f-b2ef-1c2ceffc9ea1",
"metadata": {},
"source": [
"Now we define `initial_hands(rng)` to start a new episode (Environment reset).\n",
"\n",
"It creates the initial state of a Blackjack episode:\n",
"\n",
"- player starts with 2 cards\n",
"\n",
"- dealer starts with 2 cards\n",
"\n",
"The environment internally keeps both dealer cards, but the agent will only observe one (typical Blackjack rule: one dealer card is face-up)."
]
},
{
"cell_type": "code",
"execution_count": 225,
"id": "a7debbe9-6d8f-44f4-b751-e4ccfd10ace8",
"metadata": {},
"outputs": [],
"source": [
"def initial_hands(rng: np.random.Generator) -> tuple[list[int], list[int]]:\n",
" \"\"\"Start of a Blackjack episode.\n",
"\n",
" - Player draws 2 cards\n",
" - Dealer draws 2 cards, but we only \"observe\" dealer[0]\n",
" \"\"\"\n",
" player = [draw_card(rng), draw_card(rng)]\n",
" dealer = [draw_card(rng), draw_card(rng)]\n",
" return player, dealer"
]
},
{
"cell_type": "markdown",
"id": "2197aa35-6734-4367-961a-b048802f8594",
"metadata": {},
"source": [
"Now we define the state representation for the player, which is the RL agent.\n",
"\n",
"We convert the full hands (lists of cards) into a state tuple $(p, d, u)$, where\n",
"\n",
"1. `p = sum_hand(player)`, which is Player’s current total under Blackjack rules (Ace possibly counted as 11).\n",
"2. `d = dealer[0]`, which is Dealer’s visible card (the one face-up).\n",
"3. `u = int(usable_ace(player))`, which is a binary feature : 1 if the player has a usable ace; 0 otherwise\n"
]
},
{
"cell_type": "code",
"execution_count": 226,
"id": "0f8eab84-564e-44a6-a174-7bf8d0c411dc",
"metadata": {},
"outputs": [],
"source": [
"def obs(player: list[int], dealer: list[int]) -> tuple[int, int, int]:\n",
" \"\"\"Convert internal hands into tabular state (p, d, u).\n",
"\n",
" Args:\n",
" player: list of player's cards\n",
" dealer: list of dealer's cards\n",
"\n",
" Returns:\n",
" (p, d, u): p = player's sum, d = dealer's visible card\n",
"\n",
" \"\"\"\n",
" p = sum_hand(player)\n",
" d = dealer[0]\n",
" u = int(usable_ace(player))\n",
" return (p, d, u)"
]
},
{
"cell_type": "markdown",
"id": "a23f83c4-91ee-4374-9510-e42cae3d4751",
"metadata": {},
"source": [
"### 2.2 Blackjack step function\n",
"\n",
"In reinforcement learning, an environment step function typically implements: \n",
"$$\n",
"(S_{t+1}, r_{t+1}, \\text{done})=\\text{step}(s_t, a_t)\n",
"$$\n",
"where \n",
"1. the input are the current state (here: `(player, dealer)`) and an action `(HIT or STICK)`; \n",
"2. and the output are the updated state `(player, dealer)`; the reward for this transition and a boolean `done` indicating whether the episode ended.\n",
"\n",
"In Blackjack, \n",
"1. If the player hits, the game may continue (unless the player busts).\n",
"2. If the player sticks, the dealer finishes playing, and the episode ends immediately."
]
},
{
"cell_type": "code",
"execution_count": 227,
"id": "ba254a3f-6ce3-44a3-81ff-8df9e41a11e2",
"metadata": {},
"outputs": [],
"source": [
"def step(\n",
" player: list[int],\n",
" dealer: list[int],\n",
" action: int,\n",
" rng: np.random.Generator,\n",
") -> tuple[tuple[list[int], list[int]], int, bool]:\n",
" \"\"\"Take action from current state.\n",
"\n",
" Args:\n",
" player: list of player's cards\n",
" dealer: list of dealer's cards\n",
" action: HIT or STICK\n",
" rng: random generator used to draw cards\n",
"\n",
" Returns:\n",
" next_state: (player's cards, dealer's cards)\n",
" reward: -1 (lose), 0 (draw), +1 (win)\n",
" done: True if episode ended\n",
"\n",
" \"\"\"\n",
" if action == HIT:\n",
" player.append(\n",
" draw_card(rng),\n",
" )\n",
"\n",
" if is_bust(player):\n",
" return (\n",
" (player, dealer),\n",
" -1,\n",
" True,\n",
" )\n",
" return (\n",
" (player, dealer),\n",
" 0,\n",
" False,\n",
" )\n",
"\n",
" while sum_hand(dealer) < 17: # noqa: PLR2004\n",
" dealer.append(draw_card(rng))\n",
"\n",
" ps = score(player)\n",
" ds = score(dealer)\n",
"\n",
" if ds == 0 or ps > ds:\n",
" reward = 1\n",
" elif ps < ds:\n",
" reward = -1\n",
" else:\n",
" reward = 0\n",
"\n",
" return (player, dealer), reward, True"
]
},
{
"cell_type": "markdown",
"id": "3b25f5f4-1c7d-49cc-ac32-cfe9849a0eb2",
"metadata": {},
"source": [
"-------------------\n",
"\n",
"## 3. First-visit Monte Carlo method to estimate state-value functions"
]
},
{
"cell_type": "markdown",
"id": "0efc1fe8-f848-4bdd-8568-5087438d1b9c",
"metadata": {},
"source": [
"### 3.1 Episode generation (core for Monte Carlo)\n",
"\n",
"Monte Carlo methods learn from complete episodes.\n",
"So we need a function that:\n",
"\n",
"1. starts a new game,\n",
"\n",
"2. follows a policy to generate $(S_t, A_t)$ pairs until terminal,\n",
"\n",
"3. returns the whole episode + terminal reward.\n",
"\n"
]
},
{
"cell_type": "markdown",
"id": "6c3ae6dd-98bb-4b92-b662-680b15adb185",
"metadata": {},
"source": [
"**Exercise 1.** Write a function `generate_episode` that simulates one complete Blackjack game (one episode) using a input policy. \n",
"The Args of this function `generate_episode` are \n",
"1. `policy_fn` the input policy, which is a function that takes a state $s$ and returns an action: `HIT` (1) or `STICK` (0)\n",
"2. `rng`, which is a random generator for drawing cards (so results are reproducible).\n",
"\n",
"The outputs of this function `generate_episode` are\n",
"1. `episode`: which is a list like $[(S_0, A_0), (S_1, A_1), ..., (S_{T-1}, A_{T-1})]$\n",
"2. `G`, which is the terminal return (final reward) in $\\{-1, 0,1\\}$ (lose, draw, win) since in our simplified Blackjack: intermediate rewards are 0, only the final outcome matters. \n",
"\n",
"*Remark.* In Blackjack, not all states are equally important for decision-making. When the player’s sum is below 12, hitting is always safe, since even the largest possible card (value 10) cannot make the player bust.\n",
"\n",
"As a result, there is no real choice to make in these states, and the player should always hit. For this reason, we simplify the problem by: forcing the action HIT when the player’s sum $p<12$,and only learning decisions for states with $p=12,…,21$.\n",
"\n",
"This reduces the number of states we need to consider, speeds up learning, and does not change the optimal behavior."
]
},
{
"cell_type": "code",
"execution_count": 228,
"id": "cf8415f3-97c6-4d83-b42d-4743c770abbf",
"metadata": {},
"outputs": [],
"source": [
"from collections.abc import Callable\n",
"\n",
"\n",
"def generate_episode(\n",
" policy_fn: Callable[[tuple[int, int, int]], int],\n",
" rng: np.random.Generator,\n",
") -> tuple[list[tuple[tuple[int, int, int], int]], int]:\n",
" \"\"\"Generate one full episode following a given policy.\n",
"\n",
" Hint:\n",
" - An episode is a complete Blackjack game.\n",
" - You should repeatedly:\n",
" 1) observe the current state,\n",
" 2) choose an action using the policy,\n",
" 3) apply the action to the environment,\n",
" 4) stop when the game ends.\n",
"\n",
" Returns:\n",
" episode: list of (state, action) pairs\n",
" G: terminal return (final reward), in {-1, 0, 1}\n",
"\n",
" \"\"\"\n",
" player, dealer = initial_hands(rng)\n",
"\n",
" episode = []\n",
"\n",
" while True:\n",
" s = obs(player, dealer)\n",
"\n",
" a = HIT if s[0] < 12 else policy_fn(s) # noqa: PLR2004\n",
"\n",
" episode.append((s, a))\n",
" (player, dealer), r, done = step(player, dealer, a, rng)\n",
"\n",
" if done:\n",
" return episode, r"
]
},
{
"cell_type": "markdown",
"id": "ddfb1a92-e71a-4a33-a225-695568da4e7b",
"metadata": {},
"source": [
"Test your `generate_episode` function with the following `always_hit_policy` :)."
]
},
{
"cell_type": "code",
"execution_count": 229,
"id": "4c12bb7a-76ae-4659-9064-8745ca89eef9",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Episode length: 3\n",
"Terminal return G: -1\n",
"First 3 steps: [((16, 6, 0), 1), ((20, 6, 0), 1), ((21, 6, 0), 1)]\n"
]
}
],
"source": [
"def always_hit_policy(_state: tuple[int, int, int]) -> int:\n",
" \"\"\"Return a policy that always hits.\"\"\"\n",
" return HIT\n",
"\n",
"\n",
"episode, G = generate_episode(always_hit_policy, rng)\n",
"\n",
"print(\"Episode length:\", len(episode))\n",
"print(\"Terminal return G:\", G)\n",
"print(\"First 3 steps:\", episode[:3])\n"
]
},
{
"cell_type": "markdown",
"id": "d4072bae-d975-4637-88cc-6a466a49cb76",
"metadata": {},
"source": [
"### 3.2 Estimates the state-value function of a fixed policy $\\pi$ using Monte-Carlo\n",
"\n"
]
},
{
"cell_type": "markdown",
"id": "643165a2-c569-4506-9dc5-43355e599c92",
"metadata": {},
"source": [
"In this section, we estimate the **state-value function** of a **fixed policy** using **first-visit Monte Carlo methods**.\n",
"\n",
"The goal is to approximate, for each state $s$,\n",
"$$\n",
"V_\\pi(s) = \\mathbb{E}_\\pi[G \\mid S_t = s],\n",
"$$\n",
"that is, the expected final reward obtained when starting from state $s$ and following the policy $\\pi$.\n",
"\n",
"**Key ideas**\n",
"\n",
"- We generate many **complete episodes** (full Blackjack games) by following a fixed policy.\n",
"- Each episode ends with a **terminal reward** $G \\in \\{-1, 0, 1\\}$.\n",
"- For a given state $s$, we use the observed return $G$ as a **sample** of $V_\\pi(s)$.\n",
"- In **first-visit Monte Carlo**, each state is updated **only the first time it appears in an episode**.\n",
"- The value $V_{\\pi}(s)$ is estimated by the **average of all observed returns** from first visits to $s$.\n",
"\n",
"**Important remarks** \n",
"\n",
"- This method does not require transition probabilities.\n",
"- Updates are performed **only after an episode terminates**. \n",
"- In our Blackjack setting, all intermediate rewards are zero, so the return is simply the terminal reward. Hence, we do not code it backward because, in this Blackjack setting, the return is the same for all time steps, so a backward pass brings no benefit. A forward pass is simpler and equivalent.\n"
]
},
{
"cell_type": "markdown",
"id": "0b782f88-b21e-4bd7-a4a8-ad5e57923a38",
"metadata": {},
"source": [
"**Exercise 2.** Define a `mc_prediction_first_visit()` function to estimates the state-value function of a fixed given policy $\\pi$. \n",
"\n",
"Recall that in the simplified setting of Blackjack that we use in this lab: rewards are 0 during the game, only the terminal reward is nonzero, so the return $G$ is just the final outcome in {−1,0,1}. And Monte Carlo prediction approximates the expectation by averaging returns from many episodes.\n",
"\n",
"The Args of `mc_prediction_first_visit()` are \n",
"1. `num_episodes`: Number of complete Blackjack games (episodes) to simulate. Each episode is one full game, from the initial deal until the game ends. Monte Carlo methods estimate expectations by averaging over many episodes.\n",
"A larger num_episodes gives: more accurate estimates of the value function, but higher computational cost.\n",
"\n",
"2. `rng`: random number generator, which is the source of randomness used to simulate the environment.\n",
"\n",
"The output of `mc_prediction_first_visit()` is \n",
"\n",
"`V` a dictionary mapping each state $s$ to an estimate of $V_{\\pi}(s)$. \n",
"\n",
"A example of type `dict`:"
]
},
{
"cell_type": "code",
"execution_count": 230,
"id": "14d6496d-b6fc-4130-ae59-de35b305b0a8",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"15\n"
]
}
],
"source": [
"grades = {\"Alice\": 15, \"Bob\": 12, \"Charlie\": 18}\n",
"print(grades[\"Alice\"]) # returns 15"
]
},
{
"cell_type": "code",
"execution_count": 231,
"id": "8438b2e6",
"metadata": {},
"outputs": [],
"source": [
"def target_policy(state: tuple[int, int, int]) -> int:\n",
" \"\"\"Deterministic policy: HIT if player's sum < 20 else STICK.\"\"\"\n",
" p, _d, _u = state\n",
" return HIT if p < 20 else STICK # noqa: PLR2004\n"
]
},
{
"cell_type": "code",
"execution_count": 232,
"id": "522a0b55-972e-410e-87dd-8a9fee7cf8be",
"metadata": {},
"outputs": [],
"source": [
"def mc_prediction_first_visit(\n",
" num_episodes: int = 200_000,\n",
" rng: np.random.Generator = rng,\n",
") -> dict:\n",
" \"\"\"First-visit Monte Carlo prediction for a fixed policy.\n",
"\n",
" Goal:\n",
" - Estimate the state-value function V(s) of a given policy.\n",
" - Use first-visit Monte Carlo: each state is updated at most once per episode.\n",
"\n",
" Args:\n",
" num_episodes: number of episodes to sample\n",
" rng: random generator used to draw cards\n",
"\n",
" Returns:\n",
" V: dict mapping state -> estimated value\n",
"\n",
" \"\"\"\n",
" V = defaultdict(float)\n",
" returns_sum = defaultdict(float)\n",
" returns_count = defaultdict(int)\n",
"\n",
" def pi(s: tuple[int, int, int]) -> int:\n",
" return target_policy(s)\n",
"\n",
" for _ in range(num_episodes):\n",
" episode, G = generate_episode(pi, rng)\n",
" visited_states = set()\n",
"\n",
" for s, _a in episode:\n",
" p, _d, _u = s\n",
"\n",
" if p < 12: # noqa: PLR2004\n",
" continue\n",
"\n",
" if s not in visited_states:\n",
" visited_states.add(s)\n",
" returns_sum[s] += G\n",
" returns_count[s] += 1\n",
" V[s] = returns_sum[s] / returns_count[s]\n",
" return V\n"
]
},
{
"cell_type": "markdown",
"id": "23327cd4-88b2-4f84-90d7-80a45308f99e",
"metadata": {},
"source": [
"Now we check if `mc_prediction_first_visit` is correctly defined. "
]
},
{
"cell_type": "code",
"execution_count": 233,
"id": "d81a2dd1-27ab-4b62-8b52-e0dc156b96c5",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"<class 'collections.defaultdict'> 200\n",
"0.6234567901234568\n"
]
}
],
"source": [
"V = mc_prediction_first_visit(num_episodes=10000, rng=rng)\n",
"print(type(V), len(V))\n",
"\n",
"s_test = (20, 10, 0)\n",
"\n",
"print(V[s_test])"
]
},
{
"cell_type": "markdown",
"id": "b0ea21a2-29e0-4657-a502-ef7791bfa8cb",
"metadata": {},
"source": [
"--------------------------------\n",
"\n",
"## 4. Apply Monte Carlo control to learn an optimal policy for Blackjack (with exploring starts)."
]
},
{
"cell_type": "markdown",
"id": "f0c93491-1b67-4599-84d8-ae6cffd3a126",
"metadata": {},
"source": [
"In this section, we move from **policy evaluation** to **policy control**.\n",
"\n",
"Our goal is no longer to evaluate a fixed policy, but to **learn an (approximately) optimal policy** for Blackjack directly from experience. To do this, we use **Monte Carlo control with exploring starts**.\n",
"\n",
"### Key ideas\n",
"\n",
"- We estimate the **action-value function** $Q(s,a)$, which represents the expected final reward when taking action $a$ in state $s$.\n",
"- We generate many complete episodes (full Blackjack games).\n",
"- After each episode, we update $Q(s,a)$ using the observed return.\n",
"- We then **improve the policy greedily** by choosing, in each state, the action with the highest estimated $Q$-value.\n",
"- **Exploring starts** ensure that different state–action pairs are tried, by forcing the first action of each episode to be random.\n",
"\n",
"This approach alternates between **evaluation** (updating $Q$) and **improvement** (updating the policy), gradually converging toward an optimal strategy.\n",
"\n",
"> **This exercise is more challenging than the previous ones.** \n",
"> It combines several ideas at once (episodes, first-visit Monte Carlo, action-values, and policy improvement). \n",
"> **Do not be discouraged if it does not work immediately**: take it step by step, follow the hints, and focus on understanding the logic rather than writing everything at once.\n"
]
},
{
"cell_type": "markdown",
"id": "bd3b5114-1299-4aad-a73f-0ca608c58d00",
"metadata": {},
"source": [
"**Exercise 3 ($\\star$).** Write a `mc_control_exploring_starts` function that learns an (approximately) optimal policy for Blackjack by iterating:\n",
"\n",
"1. Generate an episode using the current policy (with exploring starts)\n",
"2. Compute the return $G$ (here it’s just the terminal reward)\n",
"3. Update the action-value function $Q(s,a)$ using sample averages\n",
"4. Improve the policy to be greedy w.r.t. the updated $Q$.\n",
"\n",
"Remark. This is Monte Carlo control (not just prediction), because we are improving the policy while learning.\n",
"\n",
"The Args of this `mc_control_exploring_starts` function are \n",
"1. `num_episodes`: how many games to simulate (more = better learning, slower)\n",
"2. `rng`: random generator for reproducibility\n",
" \n",
"The outputs of this `mc_control_exploring_starts` function are \n",
"1. `Q`: mapping from (state, action) to estimated action-value\n",
" $$\n",
" Q(s,a) \\simeq \\mathbb{E}[G | S_t=s, A_t=a]\n",
" $$\n",
"2. `policy`: mapping from state to greedy action\n",
" $$\n",
" \\pi(s)=\\text{argmax}_a Q(s,a).\n",
" $$"
]
},
{
"cell_type": "markdown",
"id": "c4a77754-5e3e-4f3a-8a5c-ff1d316ad591",
"metadata": {},
"source": [
"**Hints** In the following code, \n",
"- `policy.get(s, HIT)` means: return `policy[s]` if it exists, otherwise return `HIT`.\n",
"- `visited_sa` enforces *first-visit*: each (state, action) pair is updated only once per episode.\n",
"- Sample-average update: (increment update)\n",
" $$ Q(s,a) \\leftarrow Q(s,a) + \\frac{1}{N(s,a)}(G - Q(s,a)) $$\n",
"- Greedy improvement: \n",
" $$ \\pi(s) = \\arg\\max_{a \\in \\{HIT,STICK\\}} Q(s,a) $$\n"
]
},
{
"cell_type": "code",
"execution_count": 234,
"id": "89bdd3ec",
"metadata": {},
"outputs": [],
"source": [
"def mc_control_exploring_starts(\n",
" num_episodes: int = 500_000,\n",
" rng: np.random.Generator = rng,\n",
") -> tuple[dict, dict]:\n",
" \"\"\"Monte Carlo Control with Exploring Starts (first-visit).\n",
"\n",
" Goal:\n",
" - Learn an (approximately) optimal deterministic policy for Blackjack.\n",
" - We learn Q(s,a) by averaging returns from complete episodes.\n",
" - We improve the policy by making it greedy w.r.t. Q.\n",
"\n",
" Exploring starts:\n",
" - Each episode starts from a random initial deal (random state).\n",
" - The FIRST action is chosen randomly (HIT or STICK) so that both actions\n",
" can be tried from many starting states.\n",
"\n",
" Returns:\n",
" Q: dict mapping (state, action) -> action-value estimate\n",
" policy: dict mapping state -> greedy action\n",
"\n",
" \"\"\"\n",
" Q = defaultdict(float)\n",
" Nsa = defaultdict(int)\n",
" policy = {}\n",
"\n",
" for _ in range(num_episodes):\n",
" player, dealer = initial_hands(rng)\n",
"\n",
" episode = []\n",
"\n",
" s0 = obs(player, dealer)\n",
" a0 = int(rng.integers(0, 2))\n",
"\n",
" episode.append((s0, a0))\n",
"\n",
" (player, dealer), r, done = step(player, dealer, a0, rng)\n",
"\n",
" if done:\n",
" G = r\n",
" else:\n",
" while True:\n",
" s = obs(player, dealer)\n",
"\n",
" a = HIT if s[0] < 12 else policy.get(s, HIT) # noqa: PLR2004\n",
"\n",
" episode.append((s, a))\n",
" (player, dealer), r, done = step(player, dealer, a, rng)\n",
"\n",
" if done:\n",
" G = r\n",
" break\n",
"\n",
" visited_sa = set()\n",
"\n",
" for s, a in episode:\n",
" if s[0] < 12: # noqa: PLR2004\n",
" continue\n",
"\n",
" if (s, a) in visited_sa:\n",
" continue\n",
"\n",
" visited_sa.add((s, a))\n",
" Nsa[(s, a)] += 1\n",
" Q[(s, a)] += (G - Q[(s, a)]) / Nsa[(s, a)]\n",
"\n",
" q_stick = Q[(s, STICK)]\n",
" q_hit = Q[(s, HIT)]\n",
" policy[s] = HIT if q_hit >= q_stick else STICK\n",
"\n",
" return Q, policy\n"
]
},
{
"cell_type": "code",
"execution_count": 235,
"id": "9d68d504-7596-47e4-9d72-99ea29eb3950",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0\n",
"1\n",
"3\n",
"4\n"
]
}
],
"source": [
"# A \"continue\" example :\n",
"\n",
"for i in range(5):\n",
" if i == 2: # noqa: PLR2004\n",
" continue\n",
" print(i)"
]
},
{
"cell_type": "code",
"execution_count": 236,
"id": "c381ec6a-61bd-4e51-bd95-ed7b68829e52",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(20, 10, 0) -> STICK\n",
"(13, 2, 0) -> HIT\n",
"(18, 6, 1) -> HIT\n"
]
}
],
"source": [
"# Check your mc_control_exploring_starts function.\n",
"\n",
"Q, pi_star = mc_control_exploring_starts(num_episodes=50000, rng=rng)\n",
"\n",
"# Check a few states\n",
"test_states = [(20, 10, 0), (13, 2, 0), (18, 6, 1)]\n",
"for s in test_states:\n",
" a = pi_star.get(s, None) # pi_star is a dictionary mapping states to actions.\n",
" # .get(key, default) returns: pi_star[key] if key exists, otherwise default, here it is None.\n",
" print(s, \"->\", \"HIT\" if a == HIT else \"STICK\" if a == STICK else \"unseen\")\n"
]
},
{
"cell_type": "markdown",
"id": "70fd45c8-d006-42b7-8c06-383b6fba369e",
"metadata": {},
"source": [
"-----------------------------------------------\n",
"\n",
"## 5. Address the exploration problem with $\\varepsilon$-soft policies (instead of exploring starts).\n"
]
},
{
"cell_type": "markdown",
"id": "ac79dafc-3c95-4a52-b786-41cdd2704cf1",
"metadata": {},
"source": [
"\n",
"In the previous section, we used **exploring starts** to ensure sufficient exploration when learning an optimal policy with Monte Carlo control. While exploring starts are useful for theoretical analysis, they rely on the ability to **randomly choose the initial state–action pair**, which is often unrealistic in practice.\n",
"\n",
"In this section, we address the exploration problem in a more practical way by using **$\\varepsilon$-soft ($\\varepsilon$-greedy) policies**.\n",
"\n",
"**Key ideas**\n",
"\n",
"- An **$\\varepsilon$-soft policy** assigns a nonzero probability to all actions in every state.\n",
"- With probability $1 - \\varepsilon$, the policy chooses the **greedy action** (exploitation).\n",
"- With probability $\\varepsilon$, the policy chooses a **random action** (exploration).\n",
"- (Optional) By gradually decreasing $\\varepsilon$, the policy shifts from exploration to exploitation as learning progresses.\n",
"\n",
"This approach allows the agent to explore **throughout the episode**, without requiring control over the initial state or action.\n",
"\n",
"**What you will implement**\n",
"\n",
"In the following exercises, you will:\n",
"\n",
"- Implement an **$\\varepsilon$-greedy action selection rule**.\n",
"- Use it to construct an **on-policy Monte Carlo control algorithm**.\n",
"\n",
"\n",
"*This section is conceptually challenging. Do not be discouraged if it takes time to understand how exploration and learning interact.*\n",
"\n",
"\n",
"By the end of this section, you will have implemented a fully **on-policy Monte Carlo control method** that does not rely on exploring starts and is closer to what is used in real-world reinforcement learning systems.\n",
"\n",
"\n",
"\n"
]
},
{
"cell_type": "markdown",
"id": "02b0b0e1-9922-4732-b2af-02da3c7fa3a2",
"metadata": {},
"source": [
"**Exercise 4.** In this exercise, you will define the **$\\varepsilon$-greedy policy** used for on-policy Monte Carlo control.\n",
"\n",
"Recall that the $\\varepsilon$-greedy strategy balances:\n",
"- **exploration**: trying random actions to discover new information,\n",
"- **exploitation**: choosing the action that currently looks best w.r.t. `Q`.\n",
"\n",
"More precisely, given a state $s$:\n",
"\n",
"- with probability $\\varepsilon$, choose a random action (HIT or STICK);\n",
"- with probability $1-\\varepsilon$, choose the greedy action $ \\arg\\max_a Q(s,a). $\n",
"\n",
"**Tasks**\n",
"\n",
"1. Complete the function `epsilon_greedy(Q, s, epsilon, rng)`.\n",
"2. Use `rng.random()` to decide whether to explore or exploit.\n",
"3. When exploiting, compare `Q[(s, HIT)]` and `Q[(s, STICK)]` and choose the action with the larger value.\n",
"\n",
"*Hint*\n",
"\n",
"- In Blackjack, the action space contains only two actions: `HIT` and `STICK`.\n",
"- The dictionary `Q` may contain unseen state–action pairs, which default to value 0.\n"
]
},
{
"cell_type": "code",
"execution_count": 237,
"id": "4e876128-1c6e-4c28-874d-8cb68f422d21",
"metadata": {},
"outputs": [],
"source": [
"def epsilon_greedy(Q: dict, s: tuple, epsilon: float, rng: np.random.Generator) -> int:\n",
" \"\"\"Epsilon-greedy action selection for Blackjack.\n",
"\n",
" With probability epsilon:\n",
" - choose a random action (exploration)\n",
" With probability 1 - epsilon:\n",
" - choose the greedy action argmax_a Q(s,a) (exploitation)\n",
"\n",
" Args:\n",
" Q: dict mapping (state, action) -> action-value estimate\n",
" s: current state (p, d, u)\n",
" epsilon: exploration probability in [0,1]\n",
" rng: random number generator\n",
"\n",
" Returns:\n",
" action: HIT or STICK\n",
"\n",
" \"\"\"\n",
" if rng.random() < epsilon:\n",
" return int(rng.integers(0, 2))\n",
"\n",
" q_stick = Q[(s, STICK)]\n",
" q_hit = Q[(s, HIT)]\n",
" return HIT if q_hit >= q_stick else STICK"
]
},
{
"cell_type": "markdown",
"id": "ec7a405e-36c7-4d2e-940d-3412ec68ea7c",
"metadata": {},
"source": [
"**Exercise 5.** Define a function `mc_control_epsilon_soft` that learns an (approximately) optimal Blackjack policy by repeating:\n",
"\n",
"1. Generate an episode using a $\\varepsilon$-greedy behavior policy that explores.\n",
"2. Update `Q(s,a)` using the episode return `G` with first-visit MC.\n",
"3. As learning progresses, $\\varepsilon$ decreases so the policy becomes more greedy.\n",
"\n",
"*Remark.* Unlike exploring starts, this approach does not require forcing the initial $(s,a)$. Exploration is achieved via $\\varepsilon$-greedy actions throughout the episode. Here we define a on-policy control, which means, we evaluate and improve the same policy that generates data.\n",
"\n",
"The Args of this `mc_control_epsilon_soft` function are \n",
"1. `num_episodes`: how many complete games we simulate (more = better learning, slower)\n",
"2. `N0`: a constant controlling how much exploration we do early on and how fast it decays (see the *Hint.* below).\n",
"3. `rng`: random generator for reproducibility\n",
" \n",
"The outputs of this `mc_control_epsilon_soft` function are \n",
"1. `Q`: mapping from (state, action) to estimated action-value\n",
" $$\n",
" Q(s,a) \\simeq \\mathbb{E}[G | S_t=s, A_t=a]\n",
" $$\n",
"2. `policy`: final greedy policy derived from `Q`. "
]
},
{
"cell_type": "markdown",
"id": "62819c64-d022-4c98-a0f4-ac7ae9a22dd6",
"metadata": {},
"source": [
"*Hint.* We will use the following classical exploration definition of $\\varepsilon(s)$ for a state $s$:\n",
"$$\n",
"\\varepsilon(s) = \\frac{N_0}{N_0 + N(s)},\n",
"$$\n",
"where:\n",
"- $N_0 > 0$ is a fixed constant (it is a parameter),\n",
"- $N(s)$ is the number of times state $s$ has been visited so far.\n",
"\n",
"(Why use this definition ?) This choice of $\\varepsilon(s)$ has several important properties:\n",
"\n",
"- *Pure exploration at first*: If a state has never been visited, $N(s) = 0$, then $\\varepsilon(s) = \\frac{N_0}{N_0} = 1,$ so the agent chooses actions completely at random.\n",
"\n",
"- *Gradual reduction of exploration*: As $N(s)$ increases, $\\varepsilon(s)$ decreases towards 0, and the policy becomes increasingly greedy.\n",
"\n",
"- *Controlled exploration*: The parameter $N_0$ determines how long the agent keeps exploring:\n",
" - a larger $N_0$ means **more exploration for longer**,\n",
" - a smaller $N_0$ means the policy becomes greedy **more quickly**.\n"
]
},
{
"cell_type": "code",
"execution_count": 238,
"id": "7521a88d-eed5-4415-8f61-ac4c395aff5e",
"metadata": {},
"outputs": [],
"source": [
"def mc_control_epsilon_soft(\n",
" num_episodes: int = 500_000,\n",
" N0: int = 100,\n",
" rng: np.random.Generator = rng,\n",
") -> tuple[dict, dict]:\n",
" \"\"\"On-policy first-visit Monte Carlo control using epsilon-greedy exploration.\n",
"\n",
" Args:\n",
" num_episodes: number of simulated episodes (games)\n",
" N0: controls exploration via epsilon(s) = N0 / (N0 + N(s))\n",
" rng: random generator\n",
"\n",
" Returns:\n",
" Q: dict mapping (state, action) -> action-value estimate\n",
" policy: dict mapping state -> greedy action (HIT or STICK)\n",
"\n",
" \"\"\"\n",
" Q = defaultdict(float)\n",
" Nsa = defaultdict(int)\n",
"\n",
" for _ in range(num_episodes):\n",
"\n",
" def behavior(s: tuple) -> int:\n",
" p, _d, _u = s\n",
"\n",
" if p < 12: # noqa: PLR2004\n",
" return HIT\n",
"\n",
" Ns = np.sum([Nsa[(s, a)] for a in ACTIONS])\n",
" epsilon = N0 / (N0 + Ns)\n",
"\n",
" return epsilon_greedy(Q, s, epsilon, rng)\n",
"\n",
" episode, G = generate_episode(behavior, rng)\n",
"\n",
" visited_sa = set()\n",
"\n",
" for s, a in episode:\n",
" p, _d, _u = s\n",
"\n",
" if p < 12: # noqa: PLR2004\n",
" continue\n",
"\n",
" if (s, a) in visited_sa:\n",
" continue\n",
"\n",
" visited_sa.add((s, a))\n",
"\n",
" Nsa[(s, a)] += 1\n",
"\n",
" Q[(s, a)] += (G - Q[(s, a)]) / Nsa[(s, a)]\n",
"\n",
" policy = {}\n",
"\n",
" for p in range(12, 22):\n",
" for d in range(1, 11):\n",
" for u in [0, 1]:\n",
" s = (p, d, u)\n",
"\n",
" q_stick = Q[(s, STICK)]\n",
" q_hit = Q[(s, HIT)]\n",
"\n",
" policy[s] = STICK if q_stick > q_hit else HIT\n",
"\n",
" return Q, policy\n"
]
},
{
"cell_type": "code",
"execution_count": 239,
"id": "fed938c9-3dbf-4f7c-865d-2a21206c6ff8",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Q range: [min, max] = (-1.0, 0.9687500000000001)\n"
]
}
],
"source": [
"# Quick checks for mc_control_epsilon_soft\n",
"\n",
"# Run a small training to check the function executes without errors\n",
"Q, pi_star = mc_control_epsilon_soft(num_episodes=20_000, N0=100, rng=rng)\n",
"\n",
"# Check that Q values are within the valid range [-1, 1]\n",
"# Explanation:\n",
"# In this Blackjack environment, the terminal reward is in {-1,0,1}.\n",
"# Therefore, any expected return Q(s,a) must lie between -1 and 1.\n",
"q_vals = list(Q.values())\n",
"print(\"Q range: [min, max] =\", (min(q_vals), max(q_vals)))\n",
"\n",
"assert min(q_vals) >= -1.01 and max(q_vals) <= 1.01, \"Q-values out of expected range!\" # noqa: PLR2004, PT018, S101\n"
]
},
{
"cell_type": "markdown",
"id": "f3fd5d7d-bd4c-4557-bf4f-09710844c5d1",
"metadata": {},
"source": [
"--------------------\n",
"\n"
]
},
{
"cell_type": "markdown",
"id": "7137801f-5d5d-44f5-9418-0996bbd7410e",
"metadata": {},
"source": [
"## 6. Off-Policy Monte Carlo Learning and Importance Sampling\n",
"\n",
"So far, all the algorithms we have studied were **on-policy**: the policy used to generate data (the *behavior policy*) was the same as the policy being evaluated or improved.\n",
"\n",
"In many real-world situations, however, this assumption is unrealistic. We often want to:\n",
"- evaluate or improve a **target policy**,\n",
"- using data generated by a **different behavior policy**.\n",
"\n",
"This setting is known as **off-policy learning**.\n",
"\n",
"**Key idea: separating behavior and target policies**\n",
"\n",
"- The **behavior policy** determines how data (episodes) are collected.\n",
"- The **target policy** is the policy we want to evaluate or optimize.\n",
"- In off-policy learning, these two policies are not the same.\n",
"\n",
"Because the data are generated under a different distribution than the one induced by the target policy, we must correct this mismatch.\n",
"\n",
"**Importance sampling**\n",
"\n",
"To address this issue, we use **importance sampling**, a classical statistical technique that allows expectations under one distribution to be estimated using samples from another distribution.\n",
"\n",
"In this section, you will study:\n",
"- **Ordinary importance sampling**, which uses unbiased but potentially high-variance estimates;\n",
"- **Weighted importance sampling**, which reduces variance at the cost of a small bias.\n",
"\n",
"Both methods play a central role in off-policy Monte Carlo learning.\n",
"\n",
"**What you will learn**\n",
"\n",
"In the exercises that follow, you will:\n",
"- distinguish clearly between **on-policy** and **off-policy** learning,\n",
"- evaluate a target policy using data generated by a different behavior policy,\n",
"- implement **ordinary** and **weighted importance sampling**,\n",
"- observe the bias–variance trade-off inherent in off-policy Monte Carlo methods.\n",
"\n",
"> Off-policy learning requires careful reasoning about probability distributions and can be subtle at first. \n",
"> Take your time, follow the derivations step by step, and focus on understanding *why* importance sampling is needed before worrying about implementation details.\n"
]
},
{
"cell_type": "markdown",
"id": "26b1ad91-d9dd-494b-be85-865752a9649f",
"metadata": {},
"source": [
"**Exercise 6.** (Target Policy and Behavior Policy)\n",
"\n",
"In off-policy learning, we distinguish between two different policies:\n",
"\n",
"- the **target policy** $\\pi$, which is the policy we want to evaluate or improve;\n",
"- the **behavior policy** $b$, which is the policy used to generate data (episodes).\n",
"\n",
"In this exercise, we explicitly define both policies and study their roles.\n",
"\n",
"**Target policy**: The target policy is **deterministic** and represents the strategy we want to evaluate. It is defined as:\n",
"\n",
"- **STICK** if the player’s sum $p \\ge 20$;\n",
"- **HIT** otherwise.\n",
"\n",
"**Behavior policy**: The behavior policy is $\\varepsilon$-soft and is used to generate episodes. It is defined as follows:\n",
"\n",
"- with probability $1−\\varepsilon$, follow the target policy;\n",
"- with probability $\\varepsilon$, choose a random action (HIT or STICK).\n"
]
},
{
"cell_type": "code",
"execution_count": 240,
"id": "a006d3be-3ed9-4ef2-955d-065e36fb15a3",
"metadata": {},
"outputs": [],
"source": [
"def behavior_policy(\n",
" s: tuple,\n",
" epsilon: float = 0.2,\n",
" rng: np.random.Generator = rng,\n",
") -> int:\n",
" \"\"\"ε-soft BEHAVIOR policy b.\n",
"\n",
" Rule:\n",
" - With probability (1 - epsilon), follow the target policy π\n",
" - With probability epsilon, choose a random action (HIT or STICK)\n",
"\n",
" This ensures that all actions have nonzero probability, which is\n",
" required for off-policy learning.\n",
"\n",
" Args:\n",
" s: state tuple (p, d, u)\n",
" epsilon: exploration probability\n",
" rng: random number generator\n",
"\n",
" Returns:\n",
" action: HIT or STICK\n",
"\n",
" \"\"\"\n",
" r = rng.random()\n",
"\n",
" if r < 1 - epsilon:\n",
" return target_policy(s)\n",
" return int(rng.integers(0, 2))\n"
]
},
{
"cell_type": "markdown",
"id": "8bb5136e-01f2-427d-97b9-9d3516b33c84",
"metadata": {},
"source": [
"Now we study **off-policy Monte Carlo evaluation**, where we want to estimate the value of a **target policy** using data generated by a **different behavior policy**.\n",
"\n",
"**Reminder: principle of importance sampling (IS)**\n",
"\n",
"Let:\n",
"- $\\pi$ be the **target policy** (the policy we want to evaluate),\n",
"- $b$ be the **behavior policy** (the policy used to generate data),\n",
"- $G$ be the return of an episode.\n",
"\n",
"Because episodes are generated under $b$ instead of $\\pi$, we must correct for the distribution mismatch using **importance sampling**.\n",
"\n",
"For a trajectory $(S_0,A_0,\\dots,S_{T-1},A_{T-1})$, the **importance sampling ratio** is defined as:\n",
"$$\n",
"W=\\prod_{t=0}^{T-1}\\frac{\\pi(A_t \\mid S_t)}{b(A_t \\mid S_t)}.\n",
"$$\n",
"\n",
"This ratio measures how much more likely the trajectory is under the target policy compared to the behavior policy.\n",
"\n",
"**Ordinary vs. weighted importance sampling**\n",
"\n",
"Using the importance weights $W$, we can build two estimators of\n",
"$$\n",
"V^\\pi(s_0) = \\mathbb{E}_\\pi[G \\mid S_0 = s_0].\n",
"$$\n",
"\n",
"- **Ordinary importance sampling**\n",
"$$\n",
"\\hat V_{\\text{ordinary}}=\\frac{1}{N}\\sum_{i=1}^N W^{(i)} G^{(i)}.\n",
"$$\n",
"\n",
"- **Weighted importance sampling**\n",
"$$\n",
"\\hat V_{\\text{weighted}}=\\frac{\\sum_{i=1}^N W^{(i)} G^{(i)}}{\\sum_{i=1}^N W^{(i)}}.\n",
"$$\n",
"\n",
"The ordinary estimator is unbiased but may have high variance, while the weighted estimator reduces variance at the cost of a small bias.\n",
"\n",
"**Setting of the following exercise**\n",
"\n",
"- The **target policy** $\\pi$ is deterministic.\n",
"- The **behavior policy** $b$ is $\\varepsilon$-soft:\n",
" - with probability $1-\\varepsilon$, it follows the target policy,\n",
" - with probability $\\varepsilon$, it chooses a random action.\n",
"- See **Exercise 6.**\n"
]
},
{
"cell_type": "markdown",
"id": "5c2186ad-9432-44fa-9a11-147b54d7ffb4",
"metadata": {},
"source": [
"**Exercise 7.** (Off-Policy Monte Carlo Evaluation with Importance Sampling)\n",
"\n",
"**Part 1.** Recall the importance sampling (IS) weight for a trajectory is\n",
"$$\n",
"W = \\prod_{t=0}^{T-1}\\frac{\\pi(A_t\\mid S_t)}{b(A_t\\mid S_t)}.\n",
"$$\n",
"\n",
"Because the target policy $\\pi$ is deterministic:\n",
"$$\n",
"\\pi(a\\mid s)=\n",
"\\begin{cases}\n",
"1 & \\text{if } a=\\pi(s),\\\\\n",
"0 & \\text{otherwise.}\n",
"\\end{cases}\n",
"$$\n",
"\n",
"**Question.**\n",
"1. Explain why $W=0$ as soon as the behavior policy takes an action different from the target action.\n",
"2. Show that under our behavior policy in **Exercise 6.**,\n",
"$$\n",
"b(\\pi(s)\\mid s)=(1-\\varepsilon)+\\varepsilon/2.\n",
"$$\n",
"\n",
"\n",
"**Part 2.** Off-Policy Monte Carlo Evaluation (Ordinary vs Weighted IS)\n",
"\n",
"We want to evaluate the target policy $\\pi$ using episodes generated by $b$.\n",
"\n",
"- **Ordinary IS estimator**:\n",
"$$\n",
"\\hat V_{\\text{ordinary}}=\\frac{1}{N}\\sum_{i=1}^N W^{(i)}G^{(i)}.\n",
"$$\n",
"- **Weighted IS estimator**:\n",
"$$\n",
"\\hat V_{\\text{weighted}}=\\frac{\\sum_{i=1}^N W^{(i)}G^{(i)}}{\\sum_{i=1}^N W^{(i)}}.\n",
"$$\n",
"\n",
"Here, each episode starts from the environment’s initial deal defined by `initial_hands` (see `generate_episode` function).\n"
]
},
{
"cell_type": "markdown",
"id": "81f64de2-3bc7-4491-b88c-056638912b17",
"metadata": {},
"source": [
"Define a function `off_policy_mc_eval_is` that estimate $V^\\pi(s_0) = \\mathbb{E}_\\pi[G \\mid S_0 = s_0]$, where\n",
"\n",
"- $s_0$ = `start state` that is defined in `generate_episode` function with `initial_hands`\n",
"- $\\pi$ = target_policy (the policy you want to evaluate)\n",
"- But we will not generate episodes using $\\pi$. We generate episodes using $b$ = behavior_policy, and we correct the mismatch with importance sampling.\n",
"\n",
"The Args of `off_policy_mc_eval_is` are \n",
"- num_episodes: number of episodes to simulate.\n",
"- epsilon: exploration parameter of the behavior policy $b$.\n",
"- rng: random generator.\n",
"\n",
"The outputs of `off_policy_mc_eval_is` are\n",
"\n",
"- `V_ordinary` : the Ordinary Importance Sampling estimate of $V^\\pi(s_0)$.\n",
"- `V_weighted` : the Weighted Importance Sampling estimate of $V^\\pi(s_0)$.\n"
]
},
{
"cell_type": "code",
"execution_count": 241,
"id": "6dadbb5c-1f52-4dc3-95f0-332d66876284",
"metadata": {},
"outputs": [],
"source": [
"def off_policy_mc_eval_is(\n",
" num_episodes: int = 50_000,\n",
" epsilon: float = 0.2,\n",
" rng: np.random.Generator = rng,\n",
") -> tuple[float, float]:\n",
" \"\"\"Off-policy Monte Carlo evaluation of a TARGET policy π using episodes generated by a different BEHAVIOR policy b.\n",
"\n",
" We estimate two quantities:\n",
" - V_ordinary : (1/N) * Σ_i W_i * G_i\n",
" - V_weighted : (Σ_i W_i * G_i) / (Σ_i W_i)\n",
"\n",
" where:\n",
" - G_i is the return of episode i\n",
" - W_i is the importance sampling weight:\n",
" W_i = Π_t π(A_t|S_t) / b(A_t|S_t)\n",
"\n",
" In this lab:\n",
" - π is deterministic (target_policy)\n",
" - b is epsilon-soft around π (behavior_policy)\n",
"\n",
" Args:\n",
" num_episodes (int): Number of simulated episodes.\n",
" epsilon (float): Exploration parameter for the behavior policy.\n",
" rng (np.random.Generator): Random number generator.\n",
"\n",
" Returns:\n",
" V_ordinary, V_weighted : floats\n",
"\n",
" \"\"\"\n",
" ordinary_sum = 0.0\n",
" ordinary_n = 0\n",
"\n",
" weighted_num = 0.0\n",
" weighted_den = 0.0\n",
"\n",
" for _ in range(num_episodes):\n",
" episode, G = generate_episode(\n",
" lambda s: behavior_policy(s, epsilon=epsilon, rng=rng),\n",
" rng,\n",
" )\n",
" W = 1.0\n",
"\n",
" for s, a in episode:\n",
" p, _d, _u = s\n",
"\n",
" if p < 12: # noqa: PLR2004\n",
" continue\n",
"\n",
" a_star = target_policy(s)\n",
"\n",
" if a != a_star:\n",
" W = 0.0\n",
" break\n",
"\n",
" b_prob = (1 - epsilon) + (epsilon / 2)\n",
"\n",
" W *= 1 / b_prob\n",
"\n",
" ordinary_sum += W * G\n",
" ordinary_n += 1\n",
"\n",
" weighted_num += W * G\n",
" weighted_den += W\n",
"\n",
" V_ordinary = ordinary_sum / ordinary_n\n",
" V_weighted = weighted_num / weighted_den if weighted_den > 0 else 0.0\n",
"\n",
" return V_ordinary, V_weighted\n"
]
},
{
"cell_type": "markdown",
"id": "f5ed08d2-1bce-4f26-bcc1-4cfb1c5e401d",
"metadata": {},
"source": [
"**Exercise 8.** (Variance Experiment (Ordinary vs Weighted IS))\n",
"\n",
"In this exercise, we compare the variance empirically of Ordinary vs Weighted IS.\n",
"\n",
"**Tasks.**\n",
"1. Fix $\\varepsilon=0.2$ and `num_episodes=10_000`.\n",
"2. Repeat the evaluation $K=20$ times with different random seeds.\n",
"3. Record the $K$ values of $V_{\\text{ordinary}}$ and $V_{\\text{weighted}}$.\n",
"4. Compute the empirical mean and variance of each estimator.\n",
"5. Which estimator has lower variance? \n"
]
},
{
"cell_type": "code",
"execution_count": 242,
"id": "4d3ff71b-ed58-44a5-aae5-fc5fa38a10c1",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Ordinary IS: mean = -0.30517438127233065 var = 0.0002877876907253712\n",
"Weighted IS: mean = -0.3037184822501776 var = 0.0002511580932966114\n"
]
}
],
"source": [
"def variance_experiment(\n",
" K: int = 20,\n",
" num_episodes: int = 10_000,\n",
" epsilon: float = 0.2,\n",
") -> tuple[np.ndarray, np.ndarray]:\n",
" \"\"\"Run K independent off-policy MC evaluations and report variance of estimates.\n",
"\n",
" Args:\n",
" K: number of independent runs\n",
" num_episodes: number of episodes per run\n",
" epsilon: exploration parameter for behavior policy\n",
"\n",
" Returns:\n",
" ord_vals: array of ordinary IS estimates\n",
" wgt_vals: array of weighted IS estimates\n",
"\n",
" \"\"\"\n",
" ord_vals = []\n",
" wgt_vals = []\n",
"\n",
" for k in range(K):\n",
" rng_k = np.random.default_rng(k)\n",
" V_ord, V_wgt = off_policy_mc_eval_is(\n",
" num_episodes=num_episodes,\n",
" epsilon=epsilon,\n",
" rng=rng_k,\n",
" )\n",
" ord_vals.append(V_ord)\n",
" wgt_vals.append(V_wgt)\n",
"\n",
" ord_vals = np.array(ord_vals)\n",
" wgt_vals = np.array(wgt_vals)\n",
"\n",
" print(\"Ordinary IS: mean =\", np.mean(ord_vals), \" var =\", np.var(ord_vals))\n",
" print(\"Weighted IS: mean =\", np.mean(wgt_vals), \" var =\", np.var(wgt_vals))\n",
"\n",
" return ord_vals, wgt_vals\n",
"\n",
"\n",
"ord_vals, wgt_vals = variance_experiment(K=10, num_episodes=5_000, epsilon=0.2)\n"
]
},
{
"cell_type": "markdown",
"id": "0c605809-4d2b-454e-9e4f-4e548571e4dd",
"metadata": {},
"source": [
"Now we want to learn an (approximately) optimal policy for Blackjack:\n",
"\n",
"- Learn the optimal action-value function $q_*(s,a)$ (approximated by `Q`)\n",
"\n",
"- Then take the greedy policy w.r.t. `Q` (stored in `policy`)\n",
"\n",
"But episodes are generated by a different policy:\n",
"\n",
"- **Behavior policy $b$**: $\\varepsilon$-soft (explores)\n",
"\n",
"- **Target policy $\\pi$**: greedy w.r.t. $Q$ (deterministic)\n",
"\n",
"Because data come from $b$ but we want to learn values under $\\pi$, we use importance sampling."
]
},
{
"cell_type": "markdown",
"id": "bac5048a-581c-40fc-8f99-0410bfab5d4a",
"metadata": {},
"source": [
"-----------------------\n",
"\n",
"\n",
"**Exercise 9.($\\star\\star\\star$)** (Off-Policy Monte Carlo Control (Weighted Importance Sampling))\n",
"\n",
"The goal of this exercise is to learn an approximately optimal **deterministic policy** using **off-policy Monte Carlo control** with **weighted importance sampling**.\n",
"\n",
"Let:\n",
"- **π** be the **target policy**, deterministic and greedy with respect to the action-value function `Q`,\n",
"- **b** be an **$\\varepsilon$-soft behavior policy**,\n",
"- $G \\in \\{-1, 0, 1\\}$ be the terminal return of an episode.\n",
"\n",
"Episodes are generated using the behavior policy **b**, but learning targets the policy **π**.\n",
"\n",
"**Part A — Recall Importance Sampling Weights**\n",
"\n",
"Consider one episode:\n",
"$\n",
"(s_0,a_0), (s_1,a_1), \\dots, (s_{T-1},a_{T-1})\n",
"$\n",
"with terminal return $G$.\n",
"\n",
"1. Recall the definition of the importance sampling ratio:\n",
"$$\n",
"W_t = \\prod_{k=t}^{T-1} \\frac{\\pi(a_k \\mid s_k)}{b(a_k \\mid s_k)}.\n",
"$$\n",
"\n",
"Explain why, when the target policy $\\pi$ is **deterministic**, each factor \n",
"$\\pi(a_k \\mid s_k)$ is either **1 or 0**, and consequently the full weight \n",
"$W_t$ is either **strictly positive or equal to zero**.\n",
"\n",
"**Part B — Backward Processing of Episodes**\n",
"\n",
"In the algorithm, the episode is processed **backward**, from time $T-1$ to 0.\n",
"\n",
"2. Explain why backward processing allows an **early stopping rule** when\n",
"$$\n",
"a_t \\neq \\pi(s_t).\n",
"$$\n",
"\n",
"What happens to the importance sampling weight $W_t$ after this point?\n",
"\n",
"**Part C — Weighted Incremental Update**\n",
"\n",
"For each state–action pair $(s,a)$, the algorithm maintains:\n",
"- a cumulative weight $C(s,a)$,\n",
"- an action-value estimate $Q(s,a)$.\n",
"\n",
"The update rules are:\n",
"$$\n",
"\\begin{aligned}\n",
"C(s,a) &\\leftarrow C(s,a) + W, \\\\\n",
"Q(s,a) &\\leftarrow Q(s,a) + \\frac{W}{C(s,a)}\\bigl(G - Q(s,a)\\bigr).\n",
"\\end{aligned}\n",
"$$\n",
"\n",
"3. Show that this update is an **incremental form** of the weighted average:\n",
"$$\n",
"Q(s,a) = \\frac{\\sum_i W_i G_i}{\\sum_i W_i}.\n",
"$$\n",
"\n",
"**Part D — Policy Improvement**\n",
"\n",
"After updating $Q(s,a)$, the target policy is updated as:\n",
"$$\n",
"\\pi(s) = \\arg\\max_a Q(s,a).\n",
"$$\n",
"\n",
"**Part E — Behavior Policy Probability**\n",
"\n",
"Assume that:\n",
"- the greedy action is $a^* = \\pi(s)$,\n",
"- the behavior policy selects:\n",
" - $a^* $ with probability $ 1 - \\varepsilon $,\n",
" - the other action with probability $\\varepsilon$.\n",
"\n",
"5. Compute explicitly:\n",
"$$\n",
"\\frac{\\pi(a^* \\mid s)}{b(a^* \\mid s)}\n",
"\\quad \\text{and} \\quad\n",
"\\frac{\\pi(a \\mid s)}{b(a \\mid s)} \\quad \\text{for } a \\neq a^*.\n",
"$$\n",
"\n",
"Explain why, whenever $a = a^* $, the importance weight update becomes:\n",
"$$\n",
"W \\leftarrow \\frac{W}{1 - \\varepsilon}.\n",
"$$\n",
"\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 243,
"id": "f4850733-218a-41c7-b21b-ca49234d8b4c",
"metadata": {},
"outputs": [],
"source": [
"def mc_control_off_policy(\n",
" num_episodes: int = 500_000,\n",
" epsilon: float = 0.2,\n",
" rng: np.random.Generator = rng,\n",
") -> tuple[dict, dict]:\n",
" \"\"\"Off-policy Monte Carlo control using WEIGHTED importance sampling.\n",
"\n",
" Behavior policy b:\n",
" epsilon-soft around the current target policy\n",
" Target policy pi:\n",
" deterministic, greedy w.r.t. Q\n",
"\n",
" Returns:\n",
" Q : dict mapping (state, action) -> action-value estimate\n",
" policy : dict mapping state -> greedy actio\n",
"\n",
" \"\"\"\n",
" Q = defaultdict(float)\n",
" C = defaultdict(float)\n",
" policy = {}\n",
"\n",
" def greedy_action(s: tuple) -> int:\n",
" \"\"\"Pick the greedy action based on current Q.\"\"\"\n",
" return HIT if Q[(s, HIT)] >= Q[(s, STICK)] else STICK\n",
"\n",
" def behavior_policy(s: tuple) -> int:\n",
" \"\"\"Epsilon-soft behavior policy around current target policy.\"\"\"\n",
" p, _d, _u = s\n",
" if p < 12: # noqa: PLR2004\n",
" return HIT\n",
"\n",
" a_star = policy.get(s, greedy_action(s))\n",
"\n",
" if rng.random() < 1 - epsilon:\n",
" return a_star\n",
" return STICK if a_star == HIT else HIT\n",
"\n",
" for _ in range(num_episodes):\n",
" episode, G = generate_episode(behavior_policy, rng)\n",
" W = 1.0\n",
"\n",
" for s, a in reversed(episode):\n",
" if s[0] < 12: # noqa: PLR2004\n",
" continue\n",
"\n",
" C[(s, a)] += W\n",
" Q[(s, a)] += (W / C[(s, a)]) * (G - Q[(s, a)])\n",
"\n",
" a_star = greedy_action(s)\n",
" policy[s] = a_star\n",
"\n",
" if a != a_star:\n",
" break\n",
"\n",
" W *= 1 / (1 - epsilon)\n",
"\n",
" return Q, policy\n"
]
},
{
"cell_type": "markdown",
"id": "cc2a308d-2197-46ab-a902-b1f65fbc9deb",
"metadata": {},
"source": [
"----------------------\n",
"\n",
"**Exercise 10.** (Compare off-policy MC control vs on-policy $\\varepsilon$-soft MC control)\n",
"\n",
"What will be compared?\n",
"\n",
"1. Learned policies: Do they agree on most states?\n",
"\n",
"2. Action-value functions: Are the greedy actions the same?\n",
"\n",
"3. Stability: Which method is noisier for a fixed number of episodes?\n",
"\n",
"**Step 1 — Train both algorithms**"
]
},
{
"cell_type": "code",
"execution_count": 244,
"id": "095a2741-adfc-4599-bd2a-8edc7a5174fe",
"metadata": {},
"outputs": [],
"source": [
"# Train on-policy epsilon-soft MC control\n",
"Q_on, pi_on = mc_control_epsilon_soft(\n",
" num_episodes=200_000,\n",
" N0=100,\n",
" rng=np.random.default_rng(0),\n",
")\n",
"\n",
"# Train off-policy MC control\n",
"Q_off, pi_off = mc_control_off_policy(\n",
" num_episodes=200_000,\n",
" epsilon=0.2,\n",
" rng=np.random.default_rng(0),\n",
")\n"
]
},
{
"cell_type": "markdown",
"id": "468de25e-1928-4fdf-9032-2b979c2ddefa",
"metadata": {},
"source": [
"**Step 2 — Compare greedy actions on a grid of states**"
]
},
{
"cell_type": "code",
"execution_count": 245,
"id": "e5d4f000-66a7-450b-a2aa-762375e9cbd5",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Policy agreement rate: 0.955\n"
]
}
],
"source": [
"def policy_agreement(pi1: dict, pi2: dict) -> float:\n",
" \"\"\"Compute the agreement rate between two policies.\n",
"\n",
" Args:\n",
" pi1: first policy dict mapping state -> action\n",
" pi2: second policy dict mapping state -> action\n",
"\n",
" Returns:\n",
" agreement_rate: float in [0, 1] representing the fraction of states\n",
" where both policies agree on the action.\n",
"\n",
" \"\"\"\n",
" total = 0\n",
" agree = 0\n",
"\n",
" for p in range(12, 22):\n",
" for d in range(1, 11):\n",
" for u in [0, 1]:\n",
" s = (p, d, u)\n",
" if s in pi1 and s in pi2:\n",
" total += 1\n",
" if pi1[s] == pi2[s]:\n",
" agree += 1\n",
"\n",
" return agree / total if total > 0 else 0.0\n",
"\n",
"\n",
"agreement = policy_agreement(pi_on, pi_off)\n",
"print(\"Policy agreement rate:\", agreement)\n"
]
},
{
"cell_type": "markdown",
"id": "e49d6c3f-3226-4ce4-baa8-6e7ffdc970ab",
"metadata": {},
"source": [
"**Step 3 — Inspect specific states**"
]
},
{
"cell_type": "code",
"execution_count": 246,
"id": "8632c062-a36d-4b39-aa79-f525b2d03648",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(20, 10, 0) on-policy: STICK | off-policy: STICK\n",
"(13, 2, 0) on-policy: HIT | off-policy: HIT\n",
"(18, 6, 1) on-policy: STICK | off-policy: HIT\n"
]
}
],
"source": [
"test_states = [(20, 10, 0), (13, 2, 0), (18, 6, 1)]\n",
"\n",
"for s in test_states:\n",
" print(\n",
" s,\n",
" \"on-policy:\",\n",
" \"HIT\" if pi_on.get(s) == HIT else \"STICK\",\n",
" \"| off-policy:\",\n",
" \"HIT\" if pi_off.get(s) == HIT else \"STICK\",\n",
" )\n"
]
},
{
"cell_type": "markdown",
"id": "375f68d9-f0fc-4615-b66f-3a32721c1d84",
"metadata": {},
"source": [
"**Step 4 (very slow) - Compare the stability of off-policy MC control vs on-policy $\\varepsilon$-soft MC control**"
]
},
{
"cell_type": "code",
"execution_count": 247,
"id": "b5efb0ca-8de5-432a-8aea-645820ec4961",
"metadata": {},
"outputs": [],
"source": [
"def evaluate_policy(\n",
" pi: dict,\n",
" num_eval_episodes: int = 20_000,\n",
" rng: np.random.Generator = rng,\n",
") -> float:\n",
" \"\"\"Estimate expected return of a policy by simulation. We generate episodes following pi and average terminal rewards.\"\"\"\n",
" if rng is None:\n",
" rng = np.random.default_rng(999)\n",
"\n",
" total = 0.0\n",
" for _ in range(num_eval_episodes):\n",
" _episode, G = generate_episode(policy_fn=lambda s: pi.get(s, HIT), rng=rng)\n",
" total += G\n",
" return total / num_eval_episodes\n"
]
},
{
"cell_type": "code",
"execution_count": 248,
"id": "13b72b63-375d-4150-9b83-687dc2bcb6f6",
"metadata": {},
"outputs": [],
"source": [
"def noise_experiment_performance(\n",
" K: int = 20,\n",
" train_episodes: int = 50_000,\n",
" eval_episodes: int = 20_000,\n",
" epsilon: float = 0.2,\n",
" N0: int = 100,\n",
") -> tuple[np.ndarray, np.ndarray]:\n",
" \"\"\"Compare on-policy vs off-policy MC control performance over K runs.\n",
"\n",
" Args:\n",
" K: number of independent runs\n",
" train_episodes: number of training episodes per run\n",
" eval_episodes: number of evaluation episodes per run\n",
" epsilon: exploration parameter for off-policy MC control\n",
" N0: parameter controlling exploration for on-policy MC control\n",
"\n",
" Returns:\n",
" on_perf: array of on-policy performance estimates\n",
" off_perf: array of off-policy performance estimates\n",
"\n",
" \"\"\"\n",
" on_perf = []\n",
" off_perf = []\n",
"\n",
" for k in range(K):\n",
" rng_train = np.random.default_rng(k)\n",
" rng_eval = np.random.default_rng(10_000 + k)\n",
"\n",
" _Q_on, pi_on = mc_control_epsilon_soft(\n",
" num_episodes=train_episodes,\n",
" N0=N0,\n",
" rng=rng_train,\n",
" )\n",
" on_perf.append(\n",
" evaluate_policy(pi_on, num_eval_episodes=eval_episodes, rng=rng_eval),\n",
" )\n",
"\n",
" _Q_off, pi_off = mc_control_off_policy(\n",
" num_episodes=train_episodes,\n",
" epsilon=epsilon,\n",
" rng=rng_train,\n",
" )\n",
" off_perf.append(\n",
" evaluate_policy(pi_off, num_eval_episodes=eval_episodes, rng=rng_eval),\n",
" )\n",
"\n",
" on_perf = np.array(on_perf)\n",
" off_perf = np.array(off_perf)\n",
"\n",
" print(\n",
" \"=== Estimated return: Higher mean, better policy w.r.t. the return, Low variance, better algorithm stability ===\",\n",
" )\n",
" print(f\"On-policy : mean={on_perf.mean():.4f}, var={on_perf.var():.6f}\")\n",
" print(f\"Off-policy : mean={off_perf.mean():.4f}, var={off_perf.var():.6f}\")\n",
"\n",
" return on_perf, off_perf\n"
]
},
{
"cell_type": "code",
"execution_count": 249,
"id": "8c3bbc38-926c-4af6-8f31-d7465093a84d",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"=== Estimated return: Higher mean, better policy w.r.t. the return, Low variance, better algorithm stability ===\n",
"On-policy : mean=-0.0534, var=0.000115\n",
"Off-policy : mean=-0.0360, var=0.000137\n"
]
}
],
"source": [
"on_perf, off_perf = noise_experiment_performance(\n",
" K=10,\n",
" train_episodes=50_000,\n",
" eval_episodes=10_000,\n",
" epsilon=0.2,\n",
" N0=100,\n",
")\n"
]
},
{
"cell_type": "markdown",
"id": "4b31bf12-b93b-4e93-8b5b-86a5d94d798f",
"metadata": {},
"source": [
"In fact On-policy $\\varepsilon$-soft MC control\n",
"\n",
"- Learns while exploring\n",
"- Simpler\n",
"- Usually more stable\n",
"- But policy never becomes fully greedy\n",
"\n",
"Off-policy MC control (IS)\n",
"\n",
"- Learns a deterministic greedy policy\n",
"- More flexible\n",
"\n",
"- But:\n",
" - importance weights can explode\n",
" - many episodes contribute nothing\n",
" - higher variance"
]
},
{
"cell_type": "markdown",
"id": "cb1cd119-ffca-4edb-9b46-6c6cf130a970",
"metadata": {},
"source": [
"-------------------------------\n",
"\n",
"\n",
"## 7. Plot the optimal policies and value functions "
]
},
{
"cell_type": "markdown",
"id": "9904a6af-7c92-4721-978b-114b14305957",
"metadata": {},
"source": [
"\n",
"In the Blackjack environment, states are represented by \n",
"$$\n",
"s = (\\text{player sum},\\ \\text{dealer showing},\\ \\text{usable ace}),\n",
"$$\n",
"where we consider:\n",
"- the player sum ranges from **12 to 21**,\n",
"- the dealer’s visible card ranges from **1 to 10**,\n",
"- the usable ace indicator is either **0 (no usable ace)** or **1 (usable ace)**.\n",
"\n",
"For visualization purposes, we convert value functions and policies—stored as Python dictionaries indexed by states—into **2-dimensional grids**:\n",
"\n",
"- **Rows** correspond to the player sum $$p = 12,\\dots,21$$\n",
"- **Columns** correspond to the dealer showing card $$d = 1,\\dots,10$$\n",
"\n",
"This allows us to:\n",
"- visualize **state-value functions** $$V(s)$$ as heatmaps,\n",
"- visualize **policies** as action maps (HIT or STICK),\n",
"- compare the policies and value functions learned by different Monte Carlo control methods.\n",
"\n",
"The following helper functions perform:\n",
"1. Conversion from a dictionary-based representation to a grid representation.\n",
"2. Visualization of value functions and policies using heatmaps.\n"
]
},
{
"cell_type": "code",
"execution_count": 250,
"id": "6bb5b2b6-8b7d-409b-9af1-6c6270eeaeb9",
"metadata": {},
"outputs": [],
"source": [
"def to_grid_from_V(V: dict, usable_ace_flag: int) -> np.ndarray:\n",
" \"\"\"Convert V dict into a (10 x 10) grid for plotting.\n",
"\n",
" Rows: player sum 12..21 (10 values)\n",
" Cols: dealer showing 1..10 (10 values)\n",
"\n",
" Args:\n",
" V: dict mapping state -> value\n",
" usable_ace_flag: 0 or 1 indicating whether to consider states with usable aces or not\n",
"\n",
" Returns:\n",
" grid: (10 x 10) numpy array of values\n",
"\n",
" \"\"\"\n",
" grid = np.zeros((10, 10))\n",
" for i, p in enumerate(range(12, 22)):\n",
" for j, d in enumerate(range(1, 11)):\n",
" s = (p, d, usable_ace_flag)\n",
" grid[i, j] = V.get(s, 0.0)\n",
" return grid\n",
"\n",
"\n",
"def to_grid_from_policy(policy: dict, usable_ace_flag: int) -> np.ndarray:\n",
" \"\"\"Convert policy dict into a (10 x 10) grid of actions with HIT=1, STICK=0.\n",
"\n",
" Rows: player sum 12..21 (10 values)\n",
" Cols: dealer showing 1..10 (10 values)\n",
"\n",
" Args:\n",
" policy: dict mapping state -> action\n",
" usable_ace_flag: 0 or 1 indicating whether to consider states with usable aces or not\n",
"\n",
" Returns:\n",
" grid: (10 x 10) numpy array of actions (HIT=1, STICK=0)\n",
"\n",
"\n",
" \"\"\"\n",
" grid = np.zeros((10, 10))\n",
" for i, p in enumerate(range(12, 22)):\n",
" for j, d in enumerate(range(1, 11)):\n",
" s = (p, d, usable_ace_flag)\n",
" grid[i, j] = policy.get(s, HIT)\n",
" return grid\n",
"\n",
"\n",
"def plot_value_heatmap(grid: np.ndarray, title: str = \"Value\") -> None:\n",
" \"\"\"Plot heatmap.\n",
"\n",
" Axes:\n",
" y-axis: player sum (12..21)\n",
" x-axis: dealer showing (1..10)\n",
"\n",
" Args:\n",
" grid: (10 x 10) numpy array of values\n",
" title: title of the plot\n",
"\n",
" \"\"\"\n",
" plt.figure(figsize=(7, 5))\n",
" plt.imshow(grid, origin=\"lower\", aspect=\"auto\")\n",
" plt.colorbar()\n",
" plt.xticks(ticks=np.arange(10), labels=[str(i) for i in range(1, 11)])\n",
" plt.yticks(ticks=np.arange(10), labels=[str(i) for i in range(12, 22)])\n",
" plt.xlabel(\"Dealer showing (d)\")\n",
" plt.ylabel(\"Player sum (p)\")\n",
" plt.title(title)\n",
" plt.show()\n",
"\n",
"\n",
"def plot_policy_map(grid: np.ndarray, title: str = \"Policy (1=HIT, 0=STICK)\") -> None:\n",
" \"\"\"Plot policy as a binary heatmap.\n",
"\n",
" Axes:\n",
" y-axis: player sum (12..21)\n",
" x-axis: dealer showing (1..10)\n",
"\n",
" Args:\n",
" grid: (10 x 10) numpy array of actions (HIT=1, STICK=0)\n",
" title: title of the plot\n",
"\n",
" \"\"\"\n",
" plt.figure(figsize=(7, 5))\n",
" plt.imshow(grid, origin=\"lower\", aspect=\"auto\")\n",
" plt.colorbar()\n",
" plt.xticks(ticks=np.arange(10), labels=[str(i) for i in range(1, 11)])\n",
" plt.yticks(ticks=np.arange(10), labels=[str(i) for i in range(12, 22)])\n",
" plt.xlabel(\"Dealer showing (d)\")\n",
" plt.ylabel(\"Player sum (p)\")\n",
" plt.title(title)\n",
" plt.show()\n"
]
},
{
"cell_type": "markdown",
"id": "2f0dad49-8af6-47ff-b3fb-1f0ab58f838d",
"metadata": {},
"source": [
"We now train **three different Monte Carlo control algorithms** on the Blackjack environment. \n",
"Each algorithm aims to learn an **(approximately) optimal policy** by estimating an action-value\n",
"function $Q(s,a)$ and acting greedily with respect to it.\n",
"\n",
"To ensure a fair comparison:\n",
"- All methods are trained using the **same random number generator** (fixed seed),\n",
"- The same number of episodes is used for each method,\n",
"- Each method ultimately produces a **greedy policy** derived from its learned $Q$-function.\n",
"\n",
"The three control strategies considered are:\n",
"\n",
"- **Monte Carlo Control with Exploring Starts** \n",
" Guarantees sufficient exploration by starting episodes from randomly chosen state–action pairs.\n",
"\n",
"- **On-policy Monte Carlo Control (ε-soft)** \n",
" Learns while following a stochastic ε-soft policy that balances exploration and exploitation.\n",
"\n",
"- **Off-policy Monte Carlo Control (Importance Sampling)** \n",
" Learns an optimal greedy policy while following a different exploratory behavior policy.\n",
"\n",
"The outputs of each method are:\n",
"- an estimated action-value function $ Q(s,a) $,\n",
"- a corresponding greedy policy $ \\hat{\\pi}(s) = \\arg\\max_a Q(s,a) $.\n"
]
},
{
"cell_type": "code",
"execution_count": 251,
"id": "695ee8b0-7d84-42f8-81ff-c1d5f968f381",
"metadata": {},
"outputs": [],
"source": [
"rng_train = np.random.default_rng(0)\n",
"\n",
"Q_es, pi_es = mc_control_exploring_starts(num_episodes=500_000, rng=rng_train)\n",
"Q_on, pi_on = mc_control_epsilon_soft(num_episodes=500_000, N0=100, rng=rng_train)\n",
"Q_off, pi_off = mc_control_off_policy(num_episodes=500_000, epsilon=0.2, rng=rng_train)\n",
"\n",
"policies = {\n",
" \"Exploring Starts\": pi_es,\n",
" \"On-policy ε-soft\": pi_on,\n",
" \"Off-policy IS\": pi_off,\n",
"}\n"
]
},
{
"cell_type": "markdown",
"id": "7eacd54a-73e8-480f-8f7f-a36f69e694b2",
"metadata": {},
"source": [
"**Visual Comparison of Learned Policies**\n",
"\n",
"We now visualize the **greedy policies learned by each Monte Carlo control method**.\n",
"\n",
"For each method, we plot a **policy map** showing the action selected in every state:\n",
"- **HIT (1)** or **STICK (0)**,\n",
"- for all player sums $p = 12,\\dots,21$,\n",
"- and all dealer showing cards $d = 1,\\dots,10$.\n",
"\n",
"Since the presence of a **usable ace** significantly affects the optimal decision in Blackjack,\n",
"we generate separate policy maps for:\n",
"- states **without a usable ace** (`usable_ace` = 0),\n",
"- states **with a usable ace** (`usable_ace` = 1).\n"
]
},
{
"cell_type": "code",
"execution_count": 252,
"id": "ba33e086-60b1-485f-b410-faa805457ac8",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 700x500 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 700x500 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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M9CKjr9/1HmrPGL1QeF6gNaDU2gd9fwKhOTuat6E9erLK+h5ok5j2INJzT2sctLYov7lqNjzLov/WppuceL4W3VZv6wVaA5TcaHd/PY5Zm1n0Iq41FZ41thowz5s3L9vnMytX7zDXPn29Hn1/czonL3Q+5FR7qc+juXFZ30O9nfV7JTe6n6z70CZSzzL5ex5pMKK1aVrDlJV+h3iez3nJGdKadf2cae2bZ6qBjryv+YzaIy4rzXvS/DNAUTMUQbSdXy90+utbx/bIOgK1fuHolAEX6iafF1qNrMGGPpf+otSAR39Rafd81689HdtHAySt6tekav2Fqr8eXTUFgeQxaROVjqGiORY6JIB2pdeAQccw0aDF85ehPr9efPXLVr+gPRO4A6H71S8/zX/SLtias6JfwnrR0Vo3bb7QWqdw0RoyrRHUbuR6AdVjqs03enHwHItKL4Z68dbzw9W1Xi8GnnPB+UNrW7T79siRI82FVod00NpB/QWv3d09xxfSmiEti14M9fkLYkwmra3Rc13HutELsJ4zmqybU+2c5npp85SOsaWJxhrgapOVNu1lHbcrK32teqHWYNtzcD4977SJTkd9144Ceg5NmjTJfEY8k4i1O702k+lx0ho8zYHRXJtLLrnEXcurNb9aK6T70u20ZkLH8tL8mKxTRvh7PmSlx+sf//iHGapCP8t6TuvnUp9LAzj9DOvx9IeWV1+XNq/r50Zr6rR2MGtelj/nkf5Q0h95+uNHv1f0GOvnWmu/9JzSAFfzq/KaM+QaUkDLqc+lr1OHX9CASZ8r68jy+v2lAayvMbRgU3Sqizw//PCD1adPH6tq1apW8eLFTbdQva3dY7MKVdf6hg0bWhs2bDBd2UuUKGG6E7/22mvZtj106JDVv39/q2LFiqbLcuPGjc1zZXWhrvUuCxcutK6++mrTxTUuLs5q1aqVNWvWrGz7W79+vXl8ly5dLH9l7Vp/7tw5a+rUqVbPnj3N69MuwqVKlbKaNWtmvfDCC9m6PRcUV1dqLYMOb5CQkGDKds0115hu81l9+eWXVtu2bd3HrEePHtaPP/7otY0/XetdXddHjx5t1a5d232u3XrrrdauXbuyPe/9999v9jlz5ky/X5tuP3jw4Bxf74XOZX1dnTt3NkM36Dk3aNAgc0x0O8/zTrtj63AJWm49R/R91S7reg5k7R6ekyZNmlgDBw7Mtv6LL76wGjVqZM73yy+/3AwtkbVL+7Jly8ywGNWqVTPb6V/9zO7YscOrm/mzzz7rPvf0vFu0aFG27vuBnA9Zy+Hy8ccfW+3atTPHRJf69eub90GHSgika/2DDz5ovof0XNNzbt26dUGdR1OmTLGaN29u9qdDa+j3xyOPPGLt37/fCgXtwq/fJ/odVqlSJfOaPYdvcBk1apRVo0aNCw4NAfsgGII7GIpkmzdvNl/677zzjlXY5BQcRJrhw4ebC9ipU6esSOMKhoKh55a+Ph37B4WXBnkarOm4aYALOUOICppYrnlJmhOBgqd5XZqPofkhmrdWGGnztA4DkJqaGu6iIB9Nnz7dNNFpDibgQs4QIppO+6CJu5q7pGPdBNJbCsHT3BfN/dDcME2+DXTKlWiivcH8nfsrmvkacywv42JFKw2CCISQFcEQIpqOaqtzImlPKe0hg4KlgajWmGjC9D//+c9s82ch+vgac6wwjYsF5IVD28ry9EgAQNTRoQF0Ytnc6DASwUxPAuSV9srUXrPa4881jIX2isyNjjelvRn1vNZewo8//rjp9RwIaoYAwEZ0vCrXiM1ApDl16pQZpFZHPvcnR1SHjdChKrTpU4d+WLZsmRmyRc9xHWzYX9QMAQCAiKMjtV+oZkjHAdPxxDzz/XR8MB1DTscd81ehrxnSIfp1qgkdeIwJ+QAA0UbrLHRkbR0cN+tE2fnVe/RsHiel9lX2rNfe2NhYs4SCjuCedUYFrRHSOfQCUeiDIQ2Ess6ODQBAtElLSzOjmud3IFS7Zhk5eNh7MuK80iFRso6wrvPxBTpifk50iqgqVap4rdPb6enppuekvxPxFvpgyDVFRDu5XopJzpNRAgAQic7LOVkjnwU05VFenT171gRCuzfWlLiLgquFSv/DKbWb7zFBnE6n4xKqWqFQKvTBkKt6TgOhYg6CIQBAlPlfZm9BpnrEXVQk6GDIva+4OK9gKJTi4+PN8Cue9LY+n7+1QrYIhgAAQGAyLadkWsHvI7/ppNWfffaZ17qlS5ea9YFgOg4AAODFKVZIlkBpftHmzZvN4uo6r//eu3evuZ2cnCz9+vVzb69d6n/55Rd55JFHZNu2bfL666/LBx98ICNGjAjoeQmGAABARNiwYYM0a9bMLEoHU9R/jxkzxtzWgRhdgZGqXbu26VqvtUE6PtFLL70kb775ZkBjDCmayQAAgBen+S84edmDTgOT2/CHM2bM8PmY7777ToJBMAQAALxkWpZZghHs4wsSzWQAAMDWqBkCAABe8poAnXUf0YJgCAAAZAtkMm0UDNFMBgAAbI2aIQAA4IVmMgAAYGuZ9CYDAACwj7AGQykpKdKyZUszE2/lypWlZ8+esn37dq9tpkyZYgZU0knXdJK648ePh628AADYgTNES7QIazC0cuVKGTx4sHz99ddmKO1z585Jly5d5NSpU+5tTp8+Ld26dZPHHnssnEUFAMA2Mv/XmyzYJVqENWdo8eLF2YbZ1hqijRs3yrXXXmvWDR8+3PxdsWJFWMoIAAAKt4hKoD5x4oT5W6FChTzvIyMjwywu6enpISkbAAB2kWn9dwl2H9EiYhKonU6nqQVq27atNGrUKKg8pLJly7qXhISEkJYTAIDCzknOUHho7tDWrVtl9uzZQe0nOTnZ1DC5lrS0tJCVEQAAFD4R0Uw2ZMgQWbRokaxatUouueSSoPYVGxtrFgAAkDdOcUimOILeR7QIazBkWZYMHTpU5s2bZxKka9euHc7iAAAAEXFa/12C3Ue0KBbuprGZM2fKggULzFhDBw8eNOs116dkyZLm37pOl507d5rbW7ZsMdvWqFEjqERrAACAsOcMTZo0yeT16KCKVatWdS9z5sxxbzN58mRp1qyZDBo0yNzWLvd6e+HChWEsOQAAhVfm/5rJgl2iRdibyS5k3LhxZgEAAAUjMwTBTDQFQxHTmwwAAMC2vckAAEDkcFoOswS7j2hBMAQAALzQTAYAAGAj1AwBAAAvmVLELMHIlOhBMAQAALxYIcgZ0n1EC5rJAACArVEzBAAAbJ1ATTAEAAC8ZFpFzBKMzCiam4xmMgAAYGvUDAEAAC9OcYgzyPoSp0RP1RDBEAAAsHXOEM1kAADA1qgZAgAA+ZBATTMZAACI6pwhR9D7iBY0kwEAAFujZggAAHhxhmBuMnqTAQCAqJVps5whmskAAICtUTMEAACyNZMx6CIAALCtTMthlmD3ES1oJgMAALZGzRAAAPCSGYLeZJk0kwEAgGjltIqYJbh9RE8wRDMZAACwNWqGAACAF5rJAACArTlD0BtM9xEtaCYDAAC2FtZgKCUlRVq2bCkXXXSRVK5cWXr27Cnbt2/32ubMmTMyePBgufjii6VMmTJyyy23yKFDh8JWZgAA7DLoojPIJVqEtaQrV640gc7XX38tS5culXPnzkmXLl3k1KlT7m1GjBghn3zyiXz44Ydm+/3798vNN98czmIDAGCLuckyg1yiRVhzhhYvXux1e8aMGaaGaOPGjXLttdfKiRMnZNq0aTJz5ky57rrrzDbTp0+XK664wgRQV111VbZ9ZmRkmMUlPT29AF4JAACIVhEVtmnwoypUqGD+alCktUWdO3d2b1O/fn2pUaOGrFu3Lsemt7Jly7qXhISEAio9AACFg1McIVmiRcQEQ06nU4YPHy5t27aVRo0amXUHDx6UmJgYKVeunNe2VapUMff5kpycbIIq15KWllYg5QcAoLDIpJksPDR3aOvWrbJmzZqg9hMbG2sWAACAqAmGhgwZIosWLZJVq1bJJZdc4l4fHx8vZ8+elePHj3vVDmlvMr0PAABE6qCLRSRahLWklmWZQGjevHny1VdfSe3atb3ub968uRQvXlyWLVvmXqdd7/fu3Stt2rQJQ4kBACj8nJYjJEu0KBbupjHtKbZgwQIz1pArD0gTn0uWLGn+Dhw4UEaOHGmSquPi4mTo0KEmEPLVkwwAACCqgqFJkyaZvx06dPBar93n77rrLvPvl19+WYoUKWIGW9Qu8127dpXXX389LOUFAMAOnCFoJoumQReLhbuZ7EJKlCghqampZgEAAPnPaRUxS7D7iBbRU1IAAIDC2psMAABEjkxxmCXYfUQLgiEAAOCFZjIAAAAboWYIAAB4yQxBM5fuI1oQDAEAAC80kwEAANgINUMAAMBLKGadj6ZZ66OnpAAAoEBY4hBnkIvuIy90kOVatWqZQZdbt24t69evz3X7iRMnyuWXX26m8UpISJARI0bImTNnAnpOgiEAABAR5syZY+YjHTt2rGzatEkSExPNNFyHDx/2ub3Ob/roo4+a7X/66SeZNm2a2cdjjz0W0PMSDAEAAJ/NZMEugZowYYIMGjRI+vfvLw0aNJDJkydLqVKl5K233vK5/dq1a6Vt27Zyxx13mNqkLl26SJ8+fS5Ym5QVwRAAAPDitBwhWVR6errXopOu+3L27FnZuHGjdO7c2b1OJ2rX2+vWrfP5mKuvvto8xhX8/PLLL/LZZ5/J9ddfL4EgGAIAAPlG83jKli3rXlJSUnxud/ToUcnMzJQqVap4rdfbBw8e9PkYrRF66qmnpF27dlK8eHGpW7eudOjQIeBmMnqTAQAAL5lSxCzBcD0+LS1N4uLi3OtjY2MlVFasWCHPPvusvP766ybZeufOnTJs2DB5+umn5YknnvB7PwRDAADAi2czV165Hq+BkGcwlJOKFStK0aJF5dChQ17r9XZ8fLzPx2jAc+edd8rdd99tbjdu3FhOnTol99xzj4wePdo0s/mDZjIAABB2MTEx0rx5c1m2bJl7ndPpNLfbtGnj8zGnT5/OFvBoQKUsy/L7uakZAgAAXpxSxCzByMvjtVt9UlKStGjRQlq1amXGENKaHu1dpvr16yfVq1d35x316NHD9EBr1qyZu5lMa4t0vSso8gfBEAAA8JJpOcwSjLw8vnfv3nLkyBEZM2aMSZpu2rSpLF682J1UvXfvXq+aoMcff1wcDof5u2/fPqlUqZIJhJ555pmAntdhBVKPFIW0G59mr3eQm6SYo3i4iwMAQEDOW+dkhSyQEydO+JV7E4pr5n2rb5bYMsFdMzNOnpNJ18wtkHIHi5ohAACQbwnU0YBgCAAAeLGsIuIMcqJV3Ue0iJ6SAgAA5ANqhgAAgJdMcZglGME+viARDAEAAC9OK/icH91HtKCZDAAA2Bo1QwAAwIszBAnUwT6+IBEMAQAAL05xmCUYwT6+IIU1bFu1apUZKbJatWpmBMn58+dnm5ztrrvuMveXKlVKunXrJj///HPYygsAAAqfsAZDOt9IYmKipKamZrtPB8bu2bOn/PLLL7JgwQL57rvvpGbNmtK5c2fzOAAAkL/TcWQGuUSLsDaTde/e3Sy+aA3Q119/LVu3bpWGDRuadZMmTZL4+HiZNWuW3H333QVcWgAA7MFps5yhiC1pRkaG+VuiRAn3Op2cLTY2VtasWZPr43RuFc8FAAAg6oKh+vXrS40aNSQ5OVmOHTsmZ8+elfHjx8tvv/0mBw4cyPFxKSkpZpI515KQkFCg5QYAoFAkUFtBLiRQB6948eIyd+5c2bFjh1SoUMEkUC9fvtw0q2kNUU40eNIZcl1LWlpagZYbAIBoZ/2vN1kwi+4jWkR01/rmzZvL5s2bTVCjNUOVKlWS1q1bS4sWLXJ8jDaj6QIAABDVNUOetLlLAyFNqt6wYYPcdNNN4S4SAACFljPYJrL/LdEirDVDJ0+elJ07d7pv796929QEabOY5gt9+OGHJgjSf2/ZskWGDRtmutt36dIlnMUGAKBQc9qsN1lYgyGt5enYsaP79siRI83fpKQkmTFjhkmU1nU6+GLVqlWlX79+8sQTT4SxxAAAoLAJazDUoUMHM7hiTh544AGzAACAguMMQTMXzWQAACBqOZmbDAAAwD6oGQIAAF5oJgMAALbmtFkwRDMZAACwNWqGAACAF2qGAAAAbISaIQAAYOuaIYIhAADgxQrBOEE5D6kceWgmAwAAtkbNEAAA8EIzGQAAsDWnzYIhmskAAICtUTMEAABsXTNEMAQAAGwdDNFMBgAAbI2aIQAA4MWyHGYJRrCPL0gEQwAAwIsOuBjsoIvBPr4g0UwGAABsjZohAABg6wRqgiEAAGDrnCGayQAAgK1RMwQAALzQTAYAAGzNopkMAADAPqgZAgAA2Wp1nDaqGSIYAgAAXiwTzEhQgnx4gaKZDAAA2FpYg6FVq1ZJjx49pFq1auJwOGT+/Ple9588eVKGDBkil1xyiZQsWVIaNGggkydPDlt5AQCw03QcziCXaBHWYOjUqVOSmJgoqampPu8fOXKkLF68WN577z356aefZPjw4SY4WrhwYYGXFQAAu/Ums4JcokVYc4a6d+9ulpysXbtWkpKSpEOHDub2PffcI2+88YasX79ebrzxRp+PycjIMItLenp6PpQcAAAUFhGdM3T11VebWqB9+/aJZVmyfPly2bFjh3Tp0iXHx6SkpEjZsmXdS0JCQoGWGQCAwjLoojPIJVpEdDD06quvmjwhzRmKiYmRbt26mSa1a6+9NsfHJCcny4kTJ9xLWlpagZYZAIBoZ1mhWaJFsUgPhr7++mtTO1SzZk2TcD148GCTcN25c2efj4mNjTULAABAVAdDf/75pzz22GMyb948ueGGG8y6Jk2ayObNm+XFF1/MMRgCAADBsWw2HUfEBkPnzp0zS5Ei3i15RYsWFafTGbZyAQBQ2FkEQwVHxxHauXOn+/bu3btNzU+FChWkRo0a0r59e3n44YfNGEPaTLZy5Up55513ZMKECeEsNgAAKETCGgxt2LBBOnbs6DWukNLu9DNmzJDZs2ebhOi+ffvKf/7zHxMQPfPMM3LvvfeGsdQAABRuTsshjiBrdqKpN1lYgyEdP0i7zOckPj5epk+fXqBlAgDA7qwQ9AaLpt5kEd21HgAAIKJrhnSkZ7qxAwBQGGuGHEHvo1DWDH3++ecmn6dOnTpSvHhxKVWqlMTFxZlEZ83l2b9/f/6VFAAAFAjLZnOT+RUM6Vg/9erVkwEDBkixYsVk1KhRMnfuXFmyZIm8+eabJhj68ssvTZCkyc1HjhzJ/5IDAAAUVDPZ888/Ly+//LKZVDXruD/qtttuM391DjEdNVpnmR8xYkQoygcAAAqY9b8l2H0UqmBo3bp1fu2sevXq8txzzwVbJgAAEEaWzQZdDKo3mXaLz61rPAAAQKEMhqZNmyaNGjWSEiVKmEX/rblDAACgELWTWUEuhTUYGjNmjAwbNkx69OghH374oVn035ojpPcBAIAoZ4WgJ1kem8lSU1OlVq1aprKldevWsn79+ly3P378uAwePFiqVq1qhvvRDl+fffZZ/o4zNGnSJJk6dar06dPHve7GG280M8oPHTpUnnrqqUB3CQAAIHPmzDFTc02ePNkEQhMnTpSuXbvK9u3bpXLlytm2P3v2rPzlL38x93300Ucmd3nPnj1Srly5/A2GdCb5Fi1aZFvfvHlzOX/+fKC7AwAAEcYK03QcOhH7oEGDpH///ua2BkWffvqpvPXWW/Loo49m217X69yla9euNeMfKq1VyvdmsjvvvNPUDmU1ZcoUM6EqAACIblYIB11MT0/3WnT2Cl+0lmfjxo3SuXNn9zodzkdv59SrfeHChdKmTRvTTFalShWTw/zss89KZmZm/k/HoQnUX3zxhVx11VXm9jfffCN79+6Vfv36uWeed0V4kWLeji0Sd1HkT8XWtVrTcBcBAICQSUhI8Lo9duxYGTduXLbtjh49aoIYDWo86e1t27b53Pcvv/wiX331lamM0TyhnTt3yv33329asfR58i0Y2rp1q1x55ZXm37t27TJ/K1asaBa9z8XhiJ7xBQAAgIcgEqC99iEiaWlpZuoul1DOaep0Ok2+kLZOFS1a1KTs6ADQL7zwQv4GQ8uXLw/0IQAAwKY5Q3FxcV7BUE60UkUDmkOHDnmt19vx8fE+H6M9yDRXSB/ncsUVV8jBgwdNs1tMTIxfZY38diMAAFDoxcTEmJqdZcuWedX86G3NC/Klbdu2pmlMt3PZsWOHCZL8DYT8DoZ08tXffvvN725x77//vt8FAAAAEcYKz6CLmnesw/e8/fbb8tNPP8l9990np06dcvcu09zk5ORk9/Z6v/Ym0/EPNQjSnmeaQK0J1YHwq5msUqVK0rBhQxOB6QCL2rW+WrVqZkCkY8eOyY8//ihr1qyR2bNnm/XadgcAAKKTFaa5yXr37i1HjhwxgzhrU1fTpk1l8eLF7qRq7azlOWG8JmcvWbLEDPys4x3qOEMaGI0aNSqg53VYfk4upm12OuWGBjwa/Hi66KKLTNe3u+++W7p16yaRRLvxlS1bVo7tqENvMgBA1DlvnZMVskBOnDjhV+5NKK6ZNaaMkSKlSgS1L+fpM7L3nqcKpNzB8juBWqOy0aNHm0VrgzQ6+/PPP03CU926dek9BgBAYWKJbeRpnKHy5cubBQAAFD5WmJrJwiXy240AAAAirWYIAAAUYlYImsmiqJmNYAgAAGShTVzBNnPRTAYAABAVqBkCAADeaCbL3e+//24GQ9I5yg4fPuw1BLbSkSABAEAUswiGcnXnnXeaeUAGDhxoxh4KZnyhVatWmZllN27cKAcOHJB58+ZJz5493ffntO/nn39eHn744Tw/LwAAQJ6DodWrV5upNxITEyVYOt+I7mfAgAFy8803Z7tfAyRPn3/+uQnCbrnllqCfGwAA5EDHCAp2nKAoGmco4GCofv36ZuTpUOjevbtZchIfH+91e8GCBdKxY0epU6dOSJ4fAABkpxN1+TdZV86CfXxE9yZ7/fXXzZQcK1euNPlDOo+J55JfdG40nY1Wa4Zyk5GRUWBlAgAA0S/gmqFy5cqZAOO6667zWq/zvWqOT2ZmpuSHt99+20wI66s5zVNKSoo8+eST+VIGAABswSKBOld9+/aV4sWLy8yZM4NOoA7EW2+9ZZ67RIncZ9FNTk6WkSNHum9r4JaQkFAAJQQAoJCwyBnK1datW+W7776Tyy+/XAqKJm1v375d5syZc8FtY2NjzQIAAJAvOUMtWrSQtLQ0KUjTpk2T5s2bh6QHGwAAyJ3DCs1SaGuGhg4dKsOGDTPj/DRu3Ng0mXlq0qSJ3/s6efKkGbPIZffu3bJ582apUKGC1KhRw93M9eGHH8pLL70UaFEBAEBeWOQM5ap3797mr44N5KJ5Q3lJoN6wYYPpKu/iyvVJSkqSGTNmmH/Pnj3b7LtPnz6BFhUAACD0wZDW3oRKhw4dTKCTm3vuuccsAACggFgkUOeqZs2a+VMSAAAQGSyayXL1zjvv5Hp/v379gikPAABAZAdDmjzt6dy5c3L69GmJiYmRUqVKEQwBABDtLHvVDAXctf7YsWNei/YI0zGA2rVrJ7NmzcqfUgIAgIIPhqwgl8IaDPly2WWXyXPPPZet1ggAAKDQNZPluKNixWT//v2h2h0AAAgXi95kuVq4cKHXbe0af+DAAXnttdekbdu2oSwbAAAIA0cIRpAu1CNQ9+zZ0+u2DrRYqVIlM4s9o0QDAIBoE3Aw5HQ686ckAAAgMlj0JguITr+h84lpzzIAAIBoE3AwNHz4cDOLvCsQuvbaa+XKK6+UhIQEWbFiRX6UEQAAIHKCoY8++kgSExPNvz/55BP59ddfZdu2bTJixAgZPXp0fpQRAAAUIIdHEnWeFynEwdDRo0clPj7e/Puzzz6TXr16Sb169cws9lu2bMmPMgIAgHB0rbeCXAprAnWVKlXkxx9/lKpVq8rixYtl0qRJZr1OyVG0aNH8KKOtLNm/OdxFAABEkPQ/nFK+XrhLUbgFHAz1799fbrvtNhMMabf6zp07m/XffPON1K9fPz/KCAAACpJlr95kAQdD48aNk0aNGklaWpppIouNjTXrtVbo0UcfzY8yAgCAgmQRDF3Qrbfemm1dUlJSKMoDAAAQnXOTAQCAwsHBdBwAAMDWLHs1kwU9AjUAAEA0CygYOn/+vLzzzjty6NCh/CsRAACIjJohK8ilMAZDxYoVk3vvvVfOnDmTfyUCAABh5Qh29OkQ5BxFdDNZq1atzMSsAAAAhUHACdT333+/jBw50owz1Lx5cyldurTX/U2aNAll+QAAQEGzQjCdRmGejuP22283fx944AH3Oh2J2rIs81dnsgcAAFHMsldvsoCDod27d+dPSQAAAKIhGKpZs2b+lAQAAEQEh80GXczTOEPvvvuutG3bVqpVqyZ79uwx6yZOnCgLFiwIdfkAAEBBs+han6tJkyaZBOrrr79ejh8/7s4RKleunAmIArFq1Srp0aOHCao032j+/PnZtvnpp5/kxhtvlLJly5pk7ZYtW8revXsDLTYAAEBogqFXX31Vpk6dKqNHjzYz1bu0aNFCtmzZEtC+Tp06JYmJiZKamurz/l27dkm7du2kfv36smLFCvnhhx/kiSeekBIlSgRabAAA4C8rBGMMFfYE6mbNmmVbHxsba4KbQHTv3t0sOdGAS2ugnn/+efe6unXr5rrPjIwMs7ikp6cHVCYAAGzPsldvsoBrhmrXru1z0MXFixfLFVdcEapyidPplE8//VTq1asnXbt2lcqVK0vr1q19NqV5SklJMU1qriUhISFkZQIAAIVPwMGQ5gsNHjxY5syZY8YWWr9+vTzzzDOSnJwsjzzySMgKdvjwYTl58qQ899xz0q1bN/niiy/kb3/7m9x8882ycuXKHB+n5Thx4oR70cEhAQBAACx7JVAH3Ex29913S8mSJeXxxx+X06dPyx133GESoF955RX3gIyhqhlSN910k4wYMcL8u2nTprJ27VqZPHmytG/f3ufjtLlOFwAAkDcOm3WtDzgYUn379jWLBkNae6NNWKFWsWJFMzFsgwYNvNZrU9yaNWtC/nwAAMCeAm4mGzt2rHtsoVKlSuVLIKRiYmJMN/rt27d7rd+xYwcDPwIAgPAFQzqwovbo6tSpk8ycOdOr51agtFZJk7FdCdnaU03/7RpH6OGHHza5SdqVf+fOnfLaa6/JJ598YiaLBQAA+cSyV85QwMGQBivffvutNGzYUIYNGybx8fFy3333mXWB2rBhg+mm7+qqr8nZ+u8xY8aY25owrflB2rW+cePG8uabb8rHH39sxh4CAAAIBYelXcLy6Ny5c6amZvr06bJkyRIzOOLAgQPlrrvuMt3aI4GOM6RlObajjsRdlKfZRwAACJv0P5xSvt4vpod0XFxcgVwzL330WSka5ADHmWfOyM7nHiuQcgcrqOhA4ygNiM6ePWv+Xb58edOUpWP7aPMWAACIUpY9msjyHAxt3LhRhgwZIlWrVjXd3rVpS+cQ0/F/fv75ZzPu0AMPPBD60gIAAIQ7GNLcnauuusokO0+bNs0MaqgDI1566aXubfr06SNHjhwJdVkBAEBBsOyVQB3wOEO33XabDBgwQKpXr57rGEGuQRMBAEB0cTDoYu501ngAAIDCIk8jUP/222+ycOFCMx6QJk97mjBhQqjKBgAAwsGy16z1AQdDy5YtkxtvvFHq1Kkj27Ztk0aNGsmvv/5qepNdeeWV+VNKAABQYBw2ayYLOIFaZ4V/6KGHZMuWLVKiRAkzCKImUevEqb169cqfUgIAAERKMKRd6Pv162f+rROp/vnnn1KmTBl56qmnZPz48flRRgAAYJPeZKmpqVKrVi1T4dK6dWtZv369X4+bPXu2OBwO6dmzZ/4HQ6VLl3bnCek4Q7t27XLfd/To0YALAAAAIowVnmBIB2zWqbl0UvhNmzZJYmKidO3aVQ4fPpzr4zRdR1utrrnmmjy93ICDIR1jaM2aNebf119/vTz44INmkEXtbq/3AQAA5IV2who0aJD0799fGjRoYOYnLVWqlLz11ls5PiYzM1P69u0rTz75pMlnLpAEai2ozjav9In13xrJXXbZZfQkAwCgEHCEMIFa5zvzFBsba5astNVJZ7jQ3GSXIkWKSOfOnWXdunU5Po+m6VSuXNnMjbp69eqCCYY8oy5tMtOoDQAAFCJW6LrW63ylnrQJbNy4cdk211QbreWpUqWK13q9rb3XfdGWKp0NY/PmzQU/zhAAAIA/tMe556z1vmqF8uKPP/6QO++8U6ZOnWpmvsj3YEhno9cMbX/85z//CapAAACg8NQMxcXFeQVDOdGApmjRonLo0CGv9Xo7Pj4+2/bagUsTp3v06OFe55oKTHu7b9++XerWrRu6YGjixIl+7QwAAEQ/RxgGXYyJiZHmzZubwZ1d3eM1uNHbQ4YMybZ9/fr1zZiHnh5//HFTY/TKK69ka54LOhhKSkrye4cAAAB5od3qNeZo0aKFtGrVylTGnDp1yvQuUzrOoU4Un5KSYsYh0lkwPJUrV878zbo+ZDlDGp298MILZk4yzfju1KmTSYIqWbJkQE8IAAAinBWeucl69+4tR44ckTFjxsjBgweladOmsnjxYndStc6Jqj3MQs3vYEjHEtLsb+3ipgGQVkHpIEi59f0HAADRxxHGucm0ScxXs5hasWJFro+dMWNGnp7T7/DqnXfekddff12WLFki8+fPl08++UTef/99d7ISAABANPI7GNKqKR1x2kVriLSH2f79+/OrbAAAwGZzk4WD381k58+fN8lKnooXLy7nzp3Lj3IBAACb5QxFfDBkWZbcddddXoMlnTlzRu69914zErXL3LlzQ19KAACAcAdDvrrX//3vfw91eQAAQJg5/rcEu49CFwxNnz49f0sCAAAig2WvZrLQd9YHAACIIkzUCgAAImacIdvVDK1atcpMsFatWjXTTV/HL/KkCdu63nPp1q1b2MoLAIAtWPbqWh/WYEjnG0lMTJTU1NQct9Hg58CBA+5l1qxZBVpGAABQuIW1max79+5myY125Y+Pjy+wMgEAAImqmp1Cn0Ct85BUrlxZLr/8crnvvvvk999/z3X7jIwMSU9P91oAAEDgOUOOIJdoEdHBkDaR6Zxoy5Ytk/Hjx8vKlStNTVJmZmaOj0lJSZGyZcu6l4SEhAItMwAAiC4R3Zvs9ttvd/+7cePG0qRJE6lbt66pLerUqZPPxyQnJ8vIkSPdt7VmiIAIAIAAWIwzFLHq1KkjFStWlJ07d+aaYxQXF+e1AAAA/zloJotcv/32m8kZqlq1ariLAgAAComwNpOdPHnSq5Zn9+7dsnnzZqlQoYJZnnzySbnllltMb7Jdu3bJI488Ipdeeql07do1nMUGAKBws+zVTBbWYGjDhg3SsWNH921Xro9OCjtp0iT54Ycf5O2335bjx4+bgRm7dOkiTz/9tGkKAwAA+cNhsxGowxoMdejQQSwr56O1ZMmSAi0PAACwn4juTQYAAMLAopkMAADYmWWvYCiqepMBAACEGjVDAADACwnUAADA3iyayQAAAGyDmiEAAODFYVlmCUawjy9IBEMAAMAbzWQAAAD2Qc0QAADwQm8yAABgbxbNZAAAALZBzRAAAPBCMxkAALA3i2YyAAAA26BmCAAAeKGZDAAA2JtFMxkAAIBtUDMEAACiupkrWARDAADAm06yGuxEq1E0USvNZAAAwNaoGQIAAF7oTQYAAOzNojcZAACAbVAzBAAAvDic/12CEezjCxLBEAAA8EYzGQAAgH1QMwQAAGzdmyysNUOrVq2SHj16SLVq1cThcMj8+fNz3Pbee+8120ycOLFAywgAgG0HXbSCXKJEWIOhU6dOSWJioqSmpua63bx58+Trr782QRMAAEChaSbr3r27WXKzb98+GTp0qCxZskRuuOGGC+4zIyPDLC7p6ekhKSsAAHbhoJkscjidTrnzzjvl4YcfloYNG/r1mJSUFClbtqx7SUhIyPdyAgBQKHuTWUEuUSKig6Hx48dLsWLF5IEHHvD7McnJyXLixAn3kpaWlq9lBAAA0S1ie5Nt3LhRXnnlFdm0aZNJnPZXbGysWQAAQN44aCaLDKtXr5bDhw9LjRo1TO2QLnv27JEHH3xQatWqFe7iAQBQeFn26k0WsTVDmivUuXNnr3Vdu3Y16/v37x+2cgEAgMIlrMHQyZMnZefOne7bu3fvls2bN0uFChVMjdDFF1/stX3x4sUlPj5eLr/88jCUFgAAe3DYrJksrMHQhg0bpGPHju7bI0eONH+TkpJkxowZYSwZAAA2ZtlrbrKwBkMdOnQQK4A2xV9//TVfywMAAOwnYnOGAABAeDhoJgMAALbmtP67BLuPKBGxXesBAAAKAjVDAADA1gnU1AwBAABbo2YIAAB40Umwgk6gluhBMAQAALyFYjqNKJqOg2YyAABgawRDAADA5zhDwS55kZqaaiZkL1GihLRu3VrWr1+f47ZTp06Va665RsqXL28WndM0t+1zQjAEAAB89yYLdgnQnDlzzNRcY8eOlU2bNkliYqKZpP3w4cM+t1+xYoX06dNHli9fLuvWrZOEhATp0qWL7Nu3L6DnJRgCAAARYcKECTJo0CDp37+/NGjQQCZPniylSpWSt956y+f277//vtx///3StGlTqV+/vrz55pvidDpl2bJlAT0vwRAAAPDisKyQLCo9Pd1rycjIEF/Onj0rGzduNE1dLkWKFDG3tdbHH6dPn5Zz585JhQoV/Nre/TwBbQ0AAAo/Z4gWEdN0VbZsWfeSkpLi8ymPHj0qmZmZUqVKFa/1evvgwYN+FXvUqFFSrVo1r4DKH3StBwAA+SYtLU3i4uLct2NjY/PleZ577jmZPXu2ySPS5OtAEAwBAAAvns1ceeV6vAZCnsFQTipWrChFixaVQ4cOea3X2/Hx8bk+9sUXXzTB0JdffilNmjQJuKw0kwEAgLD3JouJiZHmzZt7JT+7kqHbtGmT4+Oef/55efrpp2Xx4sXSokULyQtqhgAAQETQbvVJSUkmqGnVqpVMnDhRTp06ZXqXqX79+kn16tXdeUfjx4+XMWPGyMyZM83YRK7cojJlypjFXwRDAAAgIqbj6N27txw5csQEOBrYaJd5rfFxJVXv3bvX9DBzmTRpkumFduutt3rtR8cpGjdunN/PSzAEAAC8BDOCtOc+8mLIkCFm8UWToz39+uuvEgrkDAEAAFujZggAANh61nqCIQAA4MXh/O8SjGAfX5BoJgMAALZGzRAAAPBGMxkAALA1K/BBE33uI0rQTAYAAGyNmiEAAJBvc5NFg7DWDK1atUp69Ogh1apVE4fDIfPnz/e6X0ePrF+/vpQuXVrKly8vnTt3lm+++SZs5QUAwFY5Q1aQS5QIazCk840kJiZKamqqz/vr1asnr732mmzZskXWrFlj5h3p0qWLGaobAAAg6pvJunfvbpac3HHHHV63J0yYINOmTZMffvhBOnXqVAAlBADAhiydMj4E+4gSUZMzpBOxTZkyRcqWLWtqk3KSkZFhFpf09PQCKiEAAIWDg5yhyLJo0SIpU6aMlChRQl5++WVZunSpVKxYMcftU1JSTMDkWhISEgq0vAAAILpEfDDUsWNH2bx5s6xdu1a6desmt912mxw+fDjH7ZOTk+XEiRPuJS0trUDLCwBA4RhnyApykagR8cGQ9iS79NJL5aqrrjL5QsWKFTN/cxIbGytxcXFeCwAACIBFb7KI5nQ6vXKCAAAAojaB+uTJk7Jz50737d27d5smsQoVKsjFF18szzzzjNx4441StWpVOXr0qOmCv2/fPunVq1c4iw0AQOHm1AzoEOwjSoQ1GNqwYYPJCXIZOXKk+ZuUlCSTJ0+Wbdu2ydtvv20CIQ2OWrZsKatXr5aGDRuGsdQAABRuDpv1JgtrMNShQwexcjlYc+fOLdDyAAAA+4macYYAAEABsUKQAE3NEAAAiFqWvYKhqOtNBgAAEErUDAEAAFvXDBEMAQAAW3etp5kMAADYGjVDAADAC+MMAQAAe7PslTNEMxkAALA1aoYAAIA3p6XtXBL0PqIEwRAAAPBGMxkAAIB9UDMEAACyCEHNkO4jShAMAQAAbzSTAQAA2Ac1QwAAwEdPMHqTAQAAu7Kc/12C3UeUoJkMAADYGjVDAADA1gnUBEMAAMDWOUM0kwEAAFujZggAAHijmQwAANiaFYJgJnpiIZrJAACAvVEzBAAAvNFMBgAAbM2pAyY6Q7CP6EAzGQAAsDVqhgAAgK2bycJaM7Rq1Srp0aOHVKtWTRwOh8yfP99937lz52TUqFHSuHFjKV26tNmmX79+sn///nAWGQAA+wRDVpBLlAhrMHTq1ClJTEyU1NTUbPedPn1aNm3aJE888YT5O3fuXNm+fbvceOONYSkrAAAonMLaTNa9e3ez+FK2bFlZunSp17rXXntNWrVqJXv37pUaNWr4fFxGRoZZXNLT00NcagAACjkn03FErBMnTpjmtHLlyuW4TUpKigmkXEtCQkKBlhEAgGhnWc6QLNEiaoKhM2fOmByiPn36SFxcXI7bJScnm6DJtaSlpRVoOQEAQHSJit5kmkx92223iWVZMmnSpFy3jY2NNQsAAMgjywq+mSuKEqiLRUsgtGfPHvnqq69yrRUCAAAhYIUgZ4hgKLSB0M8//yzLly+Xiy++ONxFAgAAhUxYg6GTJ0/Kzp073bd3794tmzdvlgoVKkjVqlXl1ltvNd3qFy1aJJmZmXLw4EGznd4fExMTxpIDAFCIOZ0ijiAToKMogTqswdCGDRukY8eO7tsjR440f5OSkmTcuHGycOFCc7tp06Zej9Naog4dOhRwaQEAsAmLZrICowGNJkXnJLf7AAAACn3OEAAAKHiW0ylWkM1k0TTOEMEQAACwdTNZ1Ay6CAAAkB+oGQIAAN50wEWHfWqGCIYAAICPQMZpm2CIZjIAAGBr1AwBAAAvltMSK8hmsmgaHodgCAAAeDPd4u0zAjXNZAAAIGKkpqZKrVq1pESJEtK6dWtZv359rtt/+OGHUr9+fbN948aN5bPPPgv4OQmGAABA9mayECyBmjNnjpmaa+zYsWZu0sTEROnatascPnzY5/Zr166VPn36yMCBA+W7776Tnj17mmXr1q0BPa/DiqZGvTxIT0+XsmXLyrEddSTuImI/AEB0Sf/DKeXr/SInTpyQuLi4ArlmdpCbpJijeFD7Om+dkxWyIKBya01Qy5Yt5bXXXjO3nU6nJCQkyNChQ+XRRx/Ntn3v3r3l1KlTZkJ3l6uuusrMaTp58mS/y1roc4ZcsV76yehpuwQAwMV1/SrIuovzci7oAajNPv4XYHmKjY01S1Znz56VjRs3SnJysntdkSJFpHPnzrJu3Tqfz6HrXZO8u2hN0vz58wMqa6EPhv744w/zt+aVv4a7KAAABHU901qb/BQTEyPx8fGy5mDgeTe+lClTxtTseNImsHHjxmXb9ujRo5KZmSlVqlTxWq+3t23b5nP/Bw8e9Lm9rg9EoQ+GqlWrJmlpaXLRRReJw+EI2X410tU3WPed39WWdiprtJWXsuafaCpvNJU12spLWf9bI6SBkF7P8luJEiVk9+7dppYmVGXPeu31VSsUboU+GNIqtksuuSTf9q8nfKR/QKOxrNFWXsqaf6KpvNFU1mgrr93Lmt81QlkDIl0KWsWKFaVo0aJy6NAhr/V6W2urfNH1gWyfEzKKAQBA2GkTXfPmzWXZsmXudZpArbfbtGnj8zG63nN7tXTp0hy3t23NEAAAiA4jR46UpKQkadGihbRq1UomTpxoeov179/f3N+vXz+pXr26pKSkmNvDhg2T9u3by0svvSQ33HCDzJ49WzZs2CBTpkwJ6HkJhvJI2zw1CSwS2z6juazRVl7Kmn+iqbzRVNZoKy9ltZfevXvLkSNHZMyYMSYJWrvIL1682J0kvXfvXpP+4nL11VfLzJkz5fHHH5fHHntMLrvsMtOTrFGjRgE9b6EfZwgAACA35AwBAABbIxgCAAC2RjAEAABsjWAIAADYGsFQgFatWiU9evQwI4HqqJqBzn9SkLTroU54p6NvV65c2czku337dolEkyZNkiZNmrgHK9MxIj7//HOJBs8995w5F4YPHy6RSIe91/J5LvXr15dItW/fPvn73/8uF198sZQsWVIaN25suspGolq1amU7troMHjxYIo1Oc/DEE09I7dq1zXGtW7euPP300wU631UgdMRl/UzVrFnTlFd7DX377bcSDdcBPabaG6pq1aqm7Dq31s8//xy28uLCCIYCpOMdJCYmSmpqqkS6lStXmi/lr7/+2gxCde7cOenSpYt5DZFGRwnXoEIn6dML33XXXSc33XST/Pvf/5ZIpl/Ob7zxhgnkIlnDhg3lwIED7mXNmjUSiY4dOyZt27aV4sWLm2D4xx9/NOOHlC9fXiL1/fc8rvo5U7169ZJIM378ePOjQ2cD/+mnn8zt559/Xl599VWJRHfffbc5nu+++65s2bLFfHdpUKHBcqRfB/S4/vOf/zSzpn/zzTdSunRpM3nomTNnCrys8JN2rUfe6OGbN2+eFS0OHz5syrxy5UorGpQvX9568803rUj1xx9/WJdddpm1dOlSq3379tawYcOsSDR27FgrMTHRigajRo2y2rVrZ0UrPQfq1q1rOZ1OK9LccMMN1oABA7zW3XzzzVbfvn2tSHP69GmraNGi1qJFi7zWX3nlldbo0aOtSL4O6HsfHx9vvfDCC+51x48ft2JjY61Zs2aFqZS4EGqGbOTEiRPmb4UKFSSSaXW+jiKqv74CHVK9IGmtm454qr9WI51W0WuVfp06daRv375m4LJItHDhQjPyrNasaNNus2bNZOrUqRINdGLL9957TwYMGBDSSaFDRZuZdNqCHTt2mNvff/+9qSHs3r27RJrz58+b74Gs82Npk1Ok1mq66CSnOlig5/eCzivWunVrWbduXVjLhpwxArVN6Pwu2v6uTRCBjsxZULQqXIMfrUouU6aMzJs3Txo0aCCRSIO1TZs2RUwOQ270S3jGjBly+eWXm6acJ598Uq655hrZunWrySeLJL/88otpytEh+XU0WT2+DzzwgJmzSIfoj2SaN3L8+HG56667JBI9+uijZlZ1zRfTyTA12HjmmWdMcBxp9LzU7wLNabriiivM6MOzZs0ywcSll14qkUwDIeUaMdlFb7vuQ+QhGLIJrcXQi18k/6rSi/XmzZtNDdZHH31kLn6a9xRpAVFaWpqZD0fzGcIxs3OgPH/5a26TBkealPrBBx/IwIEDJdKCdq0ZevbZZ81trRnS81ZzLyI9GJo2bZo51loDF4n0/X7//ffN1AWaQ6afNf2BpOWNxGOruUJay6bzUGnwduWVV0qfPn1MXiEQajST2cCQIUNk0aJFsnz5cpOoHKn017/+6tNZi7UnnCYovvLKKxJp9Mv48OHD5su5WLFiZtGgTRMm9d/6izuSlStXTurVqyc7d+6USKO9b7IGv1ozEKnNei579uyRL7/80iT9RqqHH37Y1A7dfvvtpofenXfeKSNGjHBPeBlptLebfq5OnjxpfoCsX7/edALRpt5IFh8fb/4eOnTIa73edt2HyEMwVIhpbp8GQtrc9NVXX5kutdFEawkyMjIk0nTq1Mk06ekva9eitRna3KD/1l+xkUwvLrt27TKBR6TRZtyswz9ojovWZEWy6dOnmxwnzSGLVKdPn/aa4FLpuaqfs0imPbH0XNWehkuWLDG9TCOZfs9q0KP5WS7aPKm9yiI5B9LuaCbLw4XE8xe1JsvpBVCTkmvUqCGR1jSmVeILFiwwbfCu9mpN5tNExEiSnJxsmhj0GOr4IlruFStWmC+/SKPHMmvelX5h67g4kZiP9dBDD5kxUTSg2L9/v5lVWy+C2uQQabSmQhN9tZnstttuM7UBU6ZMMUuk0mBCgyFtatKawUil54DmCOlnTJvJvvvuO5kwYYJpiopE+tnXH3TafK7fuVqzpflO/fv3j/jrgDY//uMf/zAzqGtwpOM7aXOkjvWGCHXB/mbwsnz5ctOVMuuSlJRkRRpf5dRl+vTpVqTRLr81a9a0YmJirEqVKlmdOnWyvvjiCytaRHLX+t69e1tVq1Y1x7Z69erm9s6dO61I9cknn1iNGjUyXZHr169vTZkyxYpkS5YsMZ+r7du3W5EsPT3dnKM1atSwSpQoYdWpU8d0U8/IyLAi0Zw5c0wZ9bzVruqDBw82XdSj4Tqg3eufeOIJq0qVKuY81u+zSD8/7M6h/wt3QAYAABAu5AwBAABbIxgCAAC2RjAEAABsjWAIAADYGsEQAACwNYIhAABgawRDAADA1giGAACArREMAVGmVq1aMnHixAJ9Tp0axeFwyPHjxwvsOe+6664Cm77g999/N3OL/frrr34fg8WLF0vTpk0jfm4vABdGMASE4KKtF0ldihcvLlWqVJG//OUv8tZbb3GhDMIrr7wiM2bMKJDn0jm7dAJQDTT91a1bN/N+v//++/laNgD5j2AICAG9MB44cMDULHz++efSsWNHGTZsmPz1r3+V8+fPSyQ5e/asRAOdULhcuXIFMpv7tGnTZODAgXkKhP/5z3/mS7kAFByCISAEYmNjJT4+XqpXry5XXnmlPPbYY7JgwQITGHnWbmgTy9133y2VKlWSuLg4ue666+T77793379r1y5TQ6G1S2XKlJGWLVvKl19+metzX2if48aNM805b775pplBu0SJEj73s2fPHjOzefny5aV06dJmZvPPPvvMa5uNGzdKixYtpFSpUmZ2+e3bt3vdP2nSJKlbt67ExMSY2cbfffdd930PPfSQCQ5dtKlPa9O0ucnl0ksvNeX01UzWoUMHeeCBB+SRRx4xs4Pr8dbX5mnbtm3Srl078xobNGhgjp0+x/z583M8fvoa9f276qqrsq2vV6+elCxZ0gS3vprQ9Hht2LDBvG8AohfBEJBPNChJTEyUuXPnutf16tVLDh8+bIIkDSw0cOrUqZP85z//MfefPHlSrr/+elm2bJl89913psZJL7h79+7N8XkutE+1c+dO+fjjj01ZNm/e7HM/gwcPloyMDFm1apVs2bJFxo8fbwIyT6NHj5aXXnrJBADFihWTAQMGuO+bN2+eqQ178MEHZevWrfJ///d/0r9/f1m+fLm5v3379rJmzRrJzMw0t1euXCkVK1Y0uThq3759JqjQoCcnb7/9tgnUvvnmG3n++eflqaeekqVLl5r7dL8aPGmgpvdPmTLFlPdCVq9eLc2bN/dal5aWJjfffLM59nq8NNh89NFHsz22Ro0aJnDVfQCIYsFPfA/YW1JSknXTTTf5vK93797WFVdcYf69evVqKy4uzjpz5ozXNnXr1rXeeOONHPffsGFD69VXX3XfrlmzpvXyyy/7vc+xY8daxYsXtw4fPpzr62jcuLE1btw4n/ctX77c0q+LL7/80r3u008/Nev+/PNPc/vqq6+2Bg0a5PW4Xr16Wddff73597Fjx6wiRYpY3377reV0Oq0KFSpYKSkpVuvWrc397733nlW9evUcj2v79u2tdu3aee2/ZcuW1qhRo8y/P//8c6tYsWLWgQMH3PcvXbrUlHHevHk5vm59jgEDBnitS05Otho0aOC1Tp9H96Wvw1OzZs1yPG4AogM1Q0A+sizLNNMobbrSmp+LL77Y1Li4lt27d7ubWfR+bU664oorTL6M3v/TTz/lWDPkzz5VzZo1TTNabrQJ6h//+Ie0bdtWxo4dKz/88EO2bZo0aeL+d9WqVc1frZVSWk59rCe9reuVvh6tKdOaIK150qa0e+65x9SA6WvQmiKtPcqN5/O7yuB6fm2yS0hIMM1nLq1atZIL+fPPP7M1HWqZW7du7bWuTZs2Ph+vzWiadwQgehULdwGAwkwvqpqno/SCrxdvV7OQJ1eisAZC2uzz4osvmvwZvdDeeuutOSY9+7NPpU1LF6JNQV27dpVPP/1UvvjiC0lJSTFNYkOHDnVvo72nXFxBXiA95rQJTMuqOToa+GjujwZ+2nymwZA2seXG8/ldZQi2x5421R07dizPj9fmyAsFmgAiGzVDQD756quvTA3ILbfcYm5rLs/BgwdNro0GOp6LXpDVv/71L5M4/Le//U0aN25sajlyG/vGn30GQmtW7r33XpNbpIHJ1KlT/X6sBjVafk96WxOZXVx5Q5oT5coN0r+zZs2SHTt25JovdCGasK25PocOHXKv+/bbby/4uGbNmsmPP/6Y7bWsX7/ea93XX3+d7bFnzpwxNXC6DwDRi2AICAFNPNagRJOAN23aJM8++6zpFaa9p/r162e26dy5s2lq0SRfrXnRIGft2rUmyVcTktVll13mTnLWJrA77rgj15oPf/bpr+HDh8uSJUtME5u+Bk181qDAXw8//LDpOac9yn7++WeZMGGCeS1a2+Vy7bXXyh9//CGLFi3yCoZ0rB6t4dLeW3mlYztpT7akpCTTxKeB2OOPP+5Vi+WL1ob9+9//9qod0oBQX4O+Jm1+mzlzps8xjzRA0lqunJrQAEQHgiEgBLR7uF7MddA+7QGmgYSOP6Pd64sWLeq+IGt3bQ0ItJeVXvhvv/1206VdeyQpDSC0a7t2W9eeTHqh1tqfnPizT39pbyztUaYBkL4G3dfrr7/u9+M1INOBErWJT7vlv/HGGzJ9+nSv2h59bVrjpc1K9evXN+u07BrwXShf6EL0OGsXem061CEJtNnP1Zssp+EElJZHj/EHH3zg1UtMe9/p/jTPafLkySbAzUprtPr27Wt6sAGIXg7Nog53IQAgP2jtkI47pEMLaK1RTjRPSmuBdEiAIkX8+4149OhR0zSnNXCuvDAA0YkEagCFho51pL3ptLlRAyAd90h7tOUWCKkbbrjBNItpM6fmTflDmyS15oxACIh+1AwBKDTeeecdMzyADkWgCeSaU6U94nToAQDICcEQAACwNRKoAQCArREMAQAAWyMYAgAAtkYwBAAAbI1gCAAA2BrBEAAAsDWCIQAAYGsEQwAAQOzs/wFRVSWm+D5ZOwAAAABJRU5ErkJggg==",
"text/plain": [
"<Figure size 700x500 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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fvSnAW0CjX+TZWXwJhnSQSG2Kci+nnj96gXH+AtZzQ4+j+3HQY63nol4g/ckd01o3fc3a+yd9rUT6i4zmeui5p6OKa62oNv/kBj0P0pdFz0NvNTNKj4N7k6o21ep7fanPjNY66fNo85+3i7jm2jjpc+vz+HtOeTun9dxPH1z4cz6kpzV4WmatxfTWpKsjw/tKy6vvufux1uY5zRHy9zzS7xQN0PSHo7dhGtzLlVs5Q/pea+CrvfsQ+agZCjJNTnb+ynanAY9e0LZt22aGcdeaoU6dOrnGItEvKE041u7o6ce+0NoE/aWj3aK1a73mAmh38czofvXXrXY91y8f7a6v1e5a/a41Uc4v6JyiX6iakKxl1eDF2bXe+av0UjUuWhWuv7I1+VP3pU0BetymTp1qfmm6T3eg9+svQa110HGBtApfX792xdZaId2H1kLorzj9ha0Xe1/zdvQ4aaKtPk5r2DQ40nwbTe7WLtjaRVib7/QipmXWL3993aGiZdGhFLQ7uSah6/HSc8b9YqkjSM+cOdNc3LUZRs8vza3S46O/5NMnsGZFz0M9xzSg1xwXrdnUGgB9fs1Z0yYeJ01O13FrPv30U3NMfR1mIVB6Huh7oxctfe81CNRaU+dQF+lp929titImPK1B04BeP3/a3JMV3Ub3qft2z2vRC6We/4mJiSaJX4+35gqmD3y0C/mlzintYq6fBT2/dSwkPY91SA6tLXGvLfXnfEhP33/t2KHnh5Zdv3cqVapk8q20BkoDEq2h8oW+x/rDT993TcjWoUG0g4meNzpulD/nkT6vBqY6VEPDhg1NM6eeUzo4q46RpTVozh9/2c0Z0sDS+YPNOaaS7lPPV130/XGnwZS+F+QM5RGh7s6WV1yqO6fer929mzRpYroap+8mrl3l3btpOru8zpw500pMTLTKlStnFSlSxHQl37dvn8dj03etd3ZFHTp0qFWxYkWrYMGCprusdhd17y6r9Dn69+/v9TVl1rX+2LFjXl+7ezfUM2fOmP2WKlXKKlasmNW5c2drx44dZruXX345y2P5008/WcOHD7caNmxoHl+gQAHTJbhLly7Wxo0bPbY9ffq0dd9995lut7pv53HQ1/nSSy+Z2zq0gXYnXrBgQYZj5exCrsfGG+1SXatWLVMG5/uo3cG1e3716tWtwoULmzK2bt3a+u6776xQ0dek54Z2L69Xr555zTosgbeu2rt37zbDLOgx0/I3bdrUHBt3vnStd5o6dao5vvqcJUuWNN3hFy9enGE757AQDz30kM+vS/dVu3btTF9veunPZx1OoXfv3laZMmXMeahdxrVrvj5ez4X05/Dy5ctN+fR16PY9evSw/vjjD5/KOmjQIOuqq67yerzbtm1rjo8O7fDkk0+a4+Pepd3Xc2r+/Pnm/dVtdCiEMWPGmOOf/vPn6/mQvmu9k3b1v+uuu8xwAfpY3V/Xrl2tJUuWWP6YMmWK+e5xPr8e50DOIy2nvofanV6PgR4vHbJj/fr1VqCc57y3Jf3367Zt28z6UH7mEVwEQ2HK+SUVTmPZBMo5lspHH30U6qLkOZkFB+HEOf7VihUrrHDjDIZ0bKns0qBHf3hwgcz7Bg8ebAK39D8uEbnIGUKO0B4d6WmzmVbDa+8S2I826WhTcXaTyMOdvjZtlnr55ZdDXRTkIG3616ZETWqniSzvIGcIOWLs2LEmwVBzl7Tbq+ZS6aKD2qUfHwZ5m+bIaI6I5nbo9Ax5+QKS1TxheYUmRF8qkdqXcbEileaGZXe8MIQvgiHkCE0Y1wRDTYrULw7tCqzj5GiiJOxFe5LphVFrTdKPSo7Io3O/XWqQ0kgeFwv2FKVtZaEuBAAgMug4TatWrbpkk6Evw0EA6ekwFDrop7YsaC9JHR5Ch1/Iik6krD2KddJcbXnQcbq0x7Y/qBkCAPhMh7cIdEBGIDM67pkOB9OnTx+vAxGnp8OC6DAOOpelDsmyZMkSM0OBDq/gHPPOF9QMAQCAsKP5hZeqGRoxYoTJR9y6datrnY5DpYPlOicN90WerxnSEU11JFYdNC8vJ24CAPImrbPQmQh0EEp/BkYNpCn0/PnzQdlX+ilhlA6q6T5FSyB0INX0NZVaI6QDDPsjzwdDGgjRewkAkBeS1zObCDqYgdCVVYrJ4aPep6zxl3aeSN/7LpgJ9ocPHzYjrLvT2zr9jA7x4usk3Hk+GHJOVHqD3CoFpGCoiwMAgF8uygVZJV97TLydU86fP28Cob0bqkjM5YHVQqX85ZArG+0zQZxOqeIUrFqhYMrzwZCzek4DoQJRBEMAgAjzv8ze3Ez1iLk8X8DBkGtfMTEewVAw6aTDOueeO72tz+drrZAtgiEAAOCfNMshaVbg+8hpzZs3l6+//tpjnY5xp+v9wXQcAADAg0OsoCz+0vyizZs3m8XZdV7/vX//fnM7MTFRevbs6dpeu9Tv2bNHHn/8cdm+fbu8/fbb8sknn8jQoUP9el6CIQAAEBbWr18vDRo0MIvSwRT13yNHjjS3dSBGZ2CkdDR07VqvtUE6PtFrr71m5o7zZ4whRTMZAADw4DD/BSY7e2jVqpXpjp+Z6dOne33Mpk2bJBAEQwAAwEOaZZklEIE+PjfRTAYAAGyNmiEAAOAhuwnQ6fcRKQiGAABAhkAmzUbBEM1kAADA1qgZAgAAHmgmAwAAtpZGbzIAAAD7CGkwlJSUJE2aNDEz8ZYrV046d+4sO3bs8Nhm8uTJZkAlnXRNJ6k7efJkyMoLAIAdOIK0RIqQBkPLly+X/v37y9q1a81Q2hcuXJB27drJmTNnXNucPXtWOnToIE8++WQoiwoAgG2k/a83WaBLpAhpztDChQszDLOtNUQbNmyQm266yawbMmSI+bts2bKQlBEAAORtYZVAferUKfO3VKlS2d5HamqqWZxSUlKCUjYAAOwizfrvEug+IkXYJFA7HA5TC9SiRQupU6dOQHlIxYsXdy1xcXFBLScAAHmdg5yh0NDcoa1bt8qsWbMC2k9iYqKpYXIuycnJQSsjAADIe8KimWzAgAGyYMECWbFihVxxxRUB7Ss6OtosAAAgexwSJWkSFfA+IkVIgyHLsmTgwIEyZ84ckyB95ZVXhrI4AABARBzWf5dA9xEpCoS6aWzGjBkyb948M9bQ4cOHzXrN9SlSpIj5t67TZdeuXeb2li1bzLaVK1cOKNEaAAAg5DlDEydONHk9OqhihQoVXMvs2bNd20yaNEkaNGgg/fr1M7e1y73enj9/fghLDgBA3pX2v2ayQJdIEfJmsksZPXq0WQAAQO5IC0IwE0nBUNj0JgMAALBtbzIAABA+HFaUWQLdR6QgGAIAAB5oJgMAALARaoYAAICHNMlnlkCkSeQgGAIAAB6sIOQM6T4iBc1kAADA1qgZAgAAtk6gJhgCAAAe0qx8ZglEWgTNTUYzGQAAsDVqhgAAgAeHRIkjwPoSh0RO1RDBEAAAsHXOEM1kAADA1qgZAgAAOZBATTMZAACI6JyhqID3ESloJgMAALZGzRAAAPDgCMLcZPQmAwAAESvNZjlDNJMBAABbo2YIAABkaCZj0EUAAGBbaVaUWQLdR6SgmQwAANgaNUMAAMBDWhB6k6XRTAYAACKVw8pnlsD2ETnBEM1kAADA1qgZAgAAHmgmAwAAtuYIQm8w3UekoJkMAADYWkiDoaSkJGnSpIlcfvnlUq5cOencubPs2LHDY5tz585J//79pXTp0lKsWDG5++675ciRIyErMwAAdhl00RHgEilCWtLly5ebQGft2rWyePFiuXDhgrRr107OnDnj2mbo0KHy5Zdfyqeffmq2P3jwoNx1112hLDYAALaYmywtwCVShDRnaOHChR63p0+fbmqINmzYIDfddJOcOnVKpkyZIjNmzJCbb77ZbDNt2jS59tprTQB13XXXZdhnamqqWZxSUlJy4ZUAAIBIFVZhmwY/qlSpUuavBkVaW9S2bVvXNjVr1pTKlSvLmjVrMm16K168uGuJi4vLpdIDAJA3OCQqKEukCJtgyOFwyJAhQ6RFixZSp04ds+7w4cNSqFAhKVGihMe25cuXN/d5k5iYaIIq55KcnJwr5QcAIK9Io5ksNDR3aOvWrbJq1aqA9hMdHW0WAACAiAmGBgwYIAsWLJAVK1bIFVdc4VofGxsr58+fl5MnT3rUDmlvMr0PAACE66CL+SRShLSklmWZQGjOnDny/fffy5VXXulxf6NGjaRgwYKyZMkS1zrter9//35p3rx5CEoMAEDe57CigrJEigKhbhrTnmLz5s0zYw0584A08blIkSLm74MPPijDhg0zSdUxMTEycOBAEwh560kGAAAQUcHQxIkTzd9WrVp5rNfu87169TL/fv311yVfvnxmsEXtMt++fXt5++23Q1JeAADswBGEZrJIGnSxQKibyS6lcOHCMmHCBLMAAICc57DymSXQfUSKyCkpAABAXu1NBgAAwkeaRJkl0H1ECoIhAADggWYyAAAAG6FmCAAAeEgLQjOX7iNSEAwBAAAPNJMBAADYCDVDAADAQzBmnY+kWesjp6QAACBXWBIljgAX3Ud26CDLVatWNYMuN2vWTNatW5fl9uPHj5drrrnGTOMVFxcnQ4cOlXPnzvn1nARDAAAgLMyePdvMRzpq1CjZuHGjxMfHm2m4jh496nV7nd/0iSeeMNtv27ZNpkyZYvbx5JNP+vW8BEMAAMBrM1mgi7/GjRsn/fr1k969e0utWrVk0qRJUrRoUZk6darX7VevXi0tWrSQ++67z9QmtWvXTrp3737J2qT0CIYAAIAHhxUVlEWlpKR4LDrpujfnz5+XDRs2SNu2bV3rdKJ2vb1mzRqvj7n++uvNY5zBz549e+Trr7+WW2+9VfxBMAQAAHKM5vEUL17ctSQlJXnd7vjx45KWlibly5f3WK+3Dx8+7PUxWiP03HPPyQ033CAFCxaU6tWrS6tWrfxuJqM3GQAA8JAm+cwSCOfjk5OTJSYmxrU+OjpagmXZsmXy0ksvydtvv22SrXft2iWDBw+W559/Xp555hmf90MwBAAAPLg3c2WX8/EaCLkHQ5kpU6aM5M+fX44cOeKxXm/HxsZ6fYwGPA888ID07dvX3K5bt66cOXNGHnroIXnqqadMM5svaCYDAAAhV6hQIWnUqJEsWbLEtc7hcJjbzZs39/qYs2fPZgh4NKBSlmX5/NzUDAEAAA8OyWeWQGTn8dqtPiEhQRo3bixNmzY1YwhpTY/2LlM9e/aUSpUqufKOOnXqZHqgNWjQwNVMprVFut4ZFPmCYAgAAHhIs6LMEojsPL5bt25y7NgxGTlypEmarl+/vixcuNCVVL1//36PmqCnn35aoqKizN8DBw5I2bJlTSD04osv+vW8UZY/9UgRSLvxafZ6K7lDCkQVDHVxAADwy0XrgiyTeXLq1Cmfcm+Ccc18ZOVdEl0ssGtm6ukLMvHGL3Kl3IGiZggAAORYAnUkIBgCAAAeLCufOAKcaFX3ESkip6QAAAA5gJohAADgIU2izBKIQB+fmwiGAACAB4cVeM6P7iNS0EwGAABsjZohAADgwRGEBOpAH5+bCIYAAIAHh0SZJRCBPj43hTRsW7FihRkpsmLFimYEyblz52aYnK1Xr17m/qJFi0qHDh3k119/DVl5AQBA3hPSYEjnG4mPj5cJEyZkuE8Hxu7cubPs2bNH5s2bJ5s2bZIqVapI27ZtzeMAAEDOTseRFuASKULaTNaxY0ezeKM1QGvXrpWtW7dK7dq1zbqJEydKbGyszJw5U/r27ZvLpQUAwB4cNssZCtuSpqammr+FCxd2rdPJ2aKjo2XVqlVZPk7nVnFfAAAAIi4YqlmzplSuXFkSExPlxIkTcv78eRkzZoz8/vvvcujQoUwfl5SUZCaZcy5xcXG5Wm4AAPJEArUV4EICdeAKFiwoX3zxhezcuVNKlSplEqiXLl1qmtW0higzGjzpDLnOJTk5OVfLDQBApLP+15sskEX3ESnCumt9o0aNZPPmzSao0ZqhsmXLSrNmzaRx48aZPkab0XQBAACI6Johd9rcpYGQJlWvX79e7rjjjlAXCQCAPMsRaBPZ/5ZIEdKaodOnT8uuXbtct/fu3WtqgrRZTPOFPv30UxME6b+3bNkigwcPNt3t27VrF8piAwCQpzls1psspMGQ1vK0bt3adXvYsGHmb0JCgkyfPt0kSus6HXyxQoUK0rNnT3nmmWdCWGIAAJDXhDQYatWqlRlcMTODBg0yCwAAyD2OIDRz0UwGAAAiloO5yQAAAOyDmiEAAOCBZjIAAGBrDpsFQzSTAQAAW6NmCAAAeKBmCAAAwEaoGQIAALauGSIYAgAAHqwgjBOU+ZDK4YdmMgAAYGvUDAEAAA80kwEAAFtz2CwYopkMAADYmm1qhubs3CIxlxP72Vn7ivUlkiw6uFkiBccWyDkpfzmkZI3cfU6HzWqGbBMMAQAA3zhsFgxRVQIAAGyNmiEAAODBsqLMEohAH5+bCIYAAIAHHXAx0EEXA318bqKZDAAA2Bo1QwAAwNYJ1ARDAADA1jlDNJMBAABbo2YIAAB4oJkMAADYmkUzGQAAgH1QMwQAADLU6jhsVDNEMAQAADxYJpiRgAT48FxFMxkAALC1kAZDK1askE6dOknFihUlKipK5s6d63H/6dOnZcCAAXLFFVdIkSJFpFatWjJp0qSQlRcAADtNx+EIcIkUIQ2Gzpw5I/Hx8TJhwgSv9w8bNkwWLlwoH330kWzbtk2GDBligqP58+fnelkBALBbbzIrwCVShDRnqGPHjmbJzOrVqyUhIUFatWplbj/00EPyzjvvyLp16+T222/3+pjU1FSzOKWkpORAyQEAQF4R1jlD119/vakFOnDggFiWJUuXLpWdO3dKu3btMn1MUlKSFC9e3LXExcXlapkBAMgrgy46AlwiRVgHQ2+++abJE9KcoUKFCkmHDh1Mk9pNN92U6WMSExPl1KlTriU5OTlXywwAQKSzrOAskaJAuAdDa9euNbVDVapUMQnX/fv3NwnXbdu29fqY6OhoswAAAER0MPT333/Lk08+KXPmzJHbbrvNrKtXr55s3rxZXn311UyDIQAAEBjLZtNxhG0wdOHCBbPky+fZkpc/f35xOBwhKxcAAHmdRTCUe3QcoV27drlu792719T8lCpVSipXriwtW7aU4cOHmzGGtJls+fLl8sEHH8i4ceNCWWwAAJCHhDQYWr9+vbRu3dpjXCGl3emnT58us2bNMgnRPXr0kD///NMERC+++KI8/PDDISw1AAB5m8OKkqgAa3YiqTdZSIMhHT9Iu8xnJjY2VqZNm5arZQIAwO6sIPQGi6TeZGHdtR4AACCsa4Z0pGe6sQMAkBdrhqIC3keerBn65ptvTD5PtWrVpGDBglK0aFGJiYkxic6ay3Pw4MGcKykAAMgVls3mJvMpGNKxfmrUqCF9+vSRAgUKyIgRI+SLL76QRYsWyXvvvWeCoe+++84ESZrcfOzYsZwvOQAAQG41k40dO1Zef/11M6lq+nF/VNeuXc1fnUNMR43WWeaHDh0ajPIBAIBcZv1vCXQfeSoYWrNmjU87q1Spkrz88suBlgkAAISQZbNBFwPqTabd4rPqGg8AAJAng6EpU6ZInTp1pHDhwmbRf2vuEAAAyEPtZFaAS14NhkaOHCmDBw+WTp06yaeffmoW/bfmCOl9AAAgwllB6EmWzWayCRMmSNWqVU1lS7NmzWTdunVZbn/y5Enp37+/VKhQwQz3ox2+vv7665wdZ2jixIny7rvvSvfu3V3rbr/9djOj/MCBA+W5557zd5cAAAAye/ZsMzXXpEmTTCA0fvx4ad++vezYsUPKlSuXYfvz58/LLbfcYu777LPPTO7yvn37pESJEjkbDOlM8o0bN86wvlGjRnLx4kV/dwcAAMKMFaLpOHQi9n79+knv3r3NbQ2KvvrqK5k6dao88cQTGbbX9Tp36erVq834h0prlXK8meyBBx4wtUPpTZ482UyoCgAAIpsVxEEXU1JSPBadvcIbreXZsGGDtG3b1rVOh/PR25n1ap8/f740b97cNJOVL1/e5DC/9NJLkpaWlvPTcWgC9bfffivXXXeduf3DDz/I/v37pWfPnq6Z550RHhAuFh3cHOoi5FkcWwCZiYuL87g9atQoGT16dIbtjh8/boIYDWrc6e3t27d73feePXvk+++/N5Uxmie0a9cuefTRR00rlj5PjgVDW7dulYYNG5p/79692/wtU6aMWfQ+p6ioyBlfAAAAuAkgAdpjHyKSnJxspu5yCuacpg6Hw+QLaetU/vz5TcqODgD9yiuv5GwwtHTpUn8fAgAAbJozFBMT4xEMZUYrVTSgOXLkiMd6vR0bG+v1MdqDTHOF9HFO1157rRw+fNg0uxUqVCjnB10EAAAIBg1ctGZnyZIlHjU/elvzgrxp0aKFaRrT7Zx27txpgiRfAyGfgyGdfPX333/3uVvcxx9/7HMBAABAmLFCM+ii5h3r8D3vv/++bNu2TR555BE5c+aMq3eZ5iYnJia6ttf7tTeZjn+oQZD2PNMEak2o9odPzWRly5aV2rVrmwhMB1jUrvUVK1Y0AyKdOHFCfvnlF1m1apXMmjXLrNe2OwAAEJmsEM1N1q1bNzl27JgZxFmbuurXry8LFy50JVVrZy33CeM1OXvRokVm4Gcd71DHGdLAaMSIEX49b5Tl4+Ri2manU25owKPBj7vLL7/cdH3r27evdOjQQcKJduMrXry4nNhZTWIup1UQABBZUv5ySMkae+TUqVM+5d4E45pZefJIyVe0cED7cpw9J/sfei5Xyh0onxOoNSp76qmnzKK1QRqd/f333ybhqXr16vQeAwAgL7HENrI1zlDJkiXNAgAA8h4rRM1koUK7EQAAsLVs1QwBAIA8zApCM1kENbMRDAEAgHS0iSvQZi6ayQAAACICNUMAAMATzWRZ++OPP8xgSDpH2dGjRz2GwFY6EiQAAIhgFsFQlh544AEzD8iDDz5oxh4KZHyhFStWmJllN2zYIIcOHZI5c+ZI586dXfdntu+xY8fK8OHDs/28AAAA2Q6GVq5caabeiI+Pl0DpfCO6nz59+shdd92V4X4NkNx98803Jgi7++67A35uAACQCR0jKNBxgiJonCG/g6GaNWuakaeDoWPHjmbJTGxsrMftefPmSevWraVatWpBeX4AAJCRTtTl22RdmQv08WHdm+ztt982U3IsX77c5A/pPCbuS07RudF0NlqtGcpKampqrpUJAABEPr9rhkqUKGECjJtvvtljvc73qjk+aWlpkhPef/99MyGst+Y0d0lJSfLss8/mSBkAALAFiwTqLPXo0UMKFiwoM2bMCDiB2h9Tp041z124cNaz6CYmJsqwYcNctzVwi4uLy4USAgCQR1jkDGVp69atsmnTJrnmmmskt2jS9o4dO2T27NmX3DY6OtosAAAAOZIz1LhxY0lOTpbcNGXKFGnUqFFQerABAICsRVnBWfJszdDAgQNl8ODBZpyfunXrmiYzd/Xq1fN5X6dPnzZjFjnt3btXNm/eLKVKlZLKlSu7mrk+/fRTee211/wtKgAAyA6LnKEsdevWzfzVsYGcNG8oOwnU69evN13lnZy5PgkJCTJ9+nTz71mzZpl9d+/e3d+iAgAABD8Y0tqbYGnVqpUJdLLy0EMPmQUAAOQSiwTqLFWpUiVnSgIAAMKDRTNZlj744IMs7+/Zs2cg5QEAAAjvYEiTp91duHBBzp49K4UKFZKiRYsSDAEAEOkse9UM+d21/sSJEx6L9gjTMYBuuOEGmTlzZs6UEgAA5H4wZAW45NVgyJurr75aXn755Qy1RgAAAHmumSzTHRUoIAcPHgzW7gAAQKhY9CbL0vz58z1ua9f4Q4cOyVtvvSUtWrQIZtkAAEAIRAVhBOk8PQJ1586dPW7rQItly5Y1s9gzSjQAAIg0fgdDDocjZ0oCAADCg0VvMr/o9Bs6n5j2LAMAAIg0fgdDQ4YMMbPIOwOhm266SRo2bChxcXGybNmynCgjAABA+ARDn332mcTHx5t/f/nll/Lbb7/J9u3bZejQofLUU0/lRBkBAEAuinJLos72Ink4GDp+/LjExsaaf3/99dfSpUsXqVGjhpnFfsuWLTlRRgAAEIqu9VaAS14NhsqXLy+//PKLaSJbuHCh3HLLLWa9TsmRP3/+nCgjAABA+PQm6927t3Tt2lUqVKhgutW3bdvWrP/hhx+kZs2aOVFGAACQmyx79SbzOxgaPXq01KlTR5KTk00TWXR0tFmvtUJPPPFETpQRAADkJotg6JLuueeeDOsSEhKCUR4AAIDInJsMAADkDVFMxwEAAGzNslczWcAjUAMAAEQyv4KhixcvygcffCBHjhzJuRIBAIDwqBmyAlzyYjBUoEABefjhh+XcuXM5VyIAABBSUYGOPh2EnKOwbiZr2rSpmZgVAAAgL/A7gfrRRx+VYcOGmXGGGjVqJJdddpnH/fXq1Qtm+QAAQG6zgjCdRgRNx+F3MHTvvfeav4MGDXKt05GoLcsyf3WaDgAAEMEse/Um8zsY2rt3b86UBAAAIBKCoSpVquRMSQAAQFiIstmgi9kaZ+jDDz+UFi1aSMWKFWXfvn1m3fjx42XevHnBLh8AAMhtFl3rszRx4kSTQH3rrbfKyZMnXTlCJUqUMAGRP1asWCGdOnUyQZXmG82dOzfDNtu2bZPbb79dihcvbpK1mzRpIvv37/e32AAAAMEJht58801599135amnnjIz1Ts1btxYtmzZ4te+zpw5I/Hx8TJhwgSv9+/evVtuuOEGqVmzpixbtkx++ukneeaZZ6Rw4cL+FhsAAPjKCsIYQ3k9gbpBgwYZ1kdHR5vgxh8dO3Y0S2Y04NIaqLFjx7rWVa9ePct9pqammsUpJSXFrzIBAGB7lr16k/ldM3TllVd6HXRx4cKFcu211warXOJwOOSrr76SGjVqSPv27aVcuXLSrFkzr01p7pKSkkyTmnOJi4sLWpkAAEDe43cwpPlC/fv3l9mzZ5uxhdatWycvvviiJCYmyuOPPx60gh09elROnz4tL7/8snTo0EG+/fZbufPOO+Wuu+6S5cuXZ/o4LcepU6dciw4OCQAA/GDZK4Ha72ayvn37SpEiReTpp5+Ws2fPyn333WcSoN944w3XgIzBqhlSd9xxhwwdOtT8u379+rJ69WqZNGmStGzZ0uvjtLlOFwAAkD1RNuta73cwpHr06GEWDYa09kabsIKtTJkyZmLYWrVqeazXprhVq1YF/fkAAIA9+d1MNmrUKNfYQkWLFs2RQEgVKlTIdKPfsWOHx/qdO3cy8CMAAAhdMKQDK2qPrjZt2siMGTM8em75S2uVNBnbmZCtPdX0385xhIYPH25yk7Qr/65du+Stt96SL7/80kwWCwAAcohlr5whv4MhDVZ+/PFHqV27tgwePFhiY2PlkUceMev8tX79etNN39lVX5Oz9d8jR440tzVhWvODtGt93bp15b333pPPP//cjD0EAAAQDFGWdgnLpgsXLpiammnTpsmiRYvM4IgPPvig9OrVy3RrDwc6zpCW5cTOahJzebZmHwEAIGRS/nJIyRp7TA/pmJiYXLlmXvXES5I/wAGO086dk10vP5kr5Q5UQNGBxlEaEJ0/f978u2TJkqYpS8f20eYtAAAQoSx7NJFlOxjasGGDDBgwQCpUqGC6vWvTls4hpuP//Prrr2bcoUGDBgW/tAAAAKEOhjR357rrrjPJzlOmTDGDGurAiFdddZVrm+7du8uxY8eCXVYAAJAbLHslUPs9zlDXrl2lT58+UqlSpSzHCHIOmggAACJLFIMuZk1njQcAAMgrsjUC9e+//y7z58834wFp8rS7cePGBatsAAAgFCx7zVrvdzC0ZMkSuf3226VatWqyfft2qVOnjvz222+mN1nDhg1zppQAACDXRNmsmczvBGqdFf6f//ynbNmyRQoXLmwGQdQkap04tUuXLjlTSgAAgHAJhrQLfc+ePc2/dSLVv//+W4oVKybPPfecjBkzJifKCAAAbNKbbMKECVK1alVT4dKsWTNZt26dT4+bNWuWREVFSefOnXM+GLrssstceUI6ztDu3btd9x0/ftzvAgAAgDBjhSYY0gGbdWounRR+48aNEh8fL+3bt5ejR49m+ThN19FWqxtvvDFbL9fvYEjHGFq1apX596233iqPPfaYGWRRu9vrfQAAANmhnbD69esnvXv3llq1apn5SYsWLSpTp07N9DFpaWnSo0cPefbZZ00+c64kUGtBdbZ5pU+s/9ZI7uqrr6YnGQAAeUBUEBOodb4zd9HR0WZJT1uddIYLzU12ypcvn7Rt21bWrFmT6fNomk65cuXM3KgrV67MnWDIPerSJjON2gAAQB5iBa9rvc5X6k6bwEaPHp1hc0210Vqe8uXLe6zX29p73RttqdLZMDZv3pz74wwBAAD4Qnucu89a761WKDv++usveeCBB+Tdd981M1/keDCks9FrhrYv/vzzz4AKBAAA8k7NUExMjEcwlBkNaPLnzy9HjhzxWK+3Y2NjM2yvHbg0cbpTp06udc6pwLS3+44dO6R69erBC4bGjx/v084AAEDkiwrBoIuFChWSRo0amcGdnd3jNbjR2wMGDMiwfc2aNc2Yh+6efvppU2P0xhtvZGieCzgYSkhI8HmHAAAA2aHd6jXmaNy4sTRt2tRUxpw5c8b0LlM6zqFOFJ+UlGTGIdJZMNyVKFHC/E2/Pmg5QxqdvfLKK2ZOMs34btOmjUmCKlKkiF9PCAAAwpwVmrnJunXrJseOHZORI0fK4cOHpX79+rJw4UJXUrXOiao9zILN52BIxxLS7G/t4qYBkFZB6SBIWfX9BwAAkScqhHOTaZOYt2YxtWzZsiwfO3369Gw9p8/h1QcffCBvv/22LFq0SObOnStffvmlfPzxx65kJQAAgEjkczCkVVM64rST1hBpD7ODBw/mVNkAAIDN5iYLBZ+byS5evGiSldwVLFhQLly4kBPlAgAANssZCvtgyLIs6dWrl8dgSefOnZOHH37YjETt9MUXXwS/lAAAAKEOhrx1r7///vuDXR4AABBiUf9bAt1HnguGpk2blrMlAQAA4cGyVzNZ8DvrAwAARBAmagUAAGEzzpDtaoZWrFhhJlirWLGi6aav4xe504RtXe++dOjQIWTlBQDAFix7da0PaTCk843Ex8fLhAkTMt1Gg59Dhw65lpkzZ+ZqGQEAQN4W0mayjh07miUr2pU/NjY218oEAAAkomp28nwCtc5DUq5cObnmmmvkkUcekT/++CPL7VNTUyUlJcVjAQAA/ucMRQW4RIqwDoa0iUznRFuyZImMGTNGli9fbmqS0tLSMn1MUlKSFC9e3LXExcXlapkBAEBkCeveZPfee6/r33Xr1pV69epJ9erVTW1RmzZtvD4mMTFRhg0b5rqtNUMERAAA+MFinKGwVa1aNSlTpozs2rUryxyjmJgYjwUAAPguimay8PX777+bnKEKFSqEuigAACCPCGkz2enTpz1qefbu3SubN2+WUqVKmeXZZ5+Vu+++2/Qm2717tzz++ONy1VVXSfv27UNZbAAA8jbLXs1kIQ2G1q9fL61bt3bddub66KSwEydOlJ9++knef/99OXnypBmYsV27dvL888+bpjAAAJAzomw2AnVIg6FWrVqJZWV+tBYtWpSr5QEAAPYT1r3JAABACFg0kwEAADuz7BUMRVRvMgAAgGCjZggAAHgggRoAANibRTMZAACAbVAzBAAAPERZllkCEejjcxPBEAAA8EQzGQAAgH1QMwQAADzQmwwAANibRTMZAACAbVAzBAAAPNBMBgAA7M2imQwAAMA2qBkCAAAeaCYDAAD2ZtFMBgAAYBvUDAEAgIhu5goUwRAAAPCkk6wGOtFqBE3USjMZAACwNWqGAACAB3qTAQAAe7PoTQYAAGAb1AwBAAAPUY7/LoEI9PG5iWAIAAB4opkMAADAPqgZAgAAtu5NFtKaoRUrVkinTp2kYsWKEhUVJXPnzs1024cffthsM378+FwtIwAAth100QpwiRAhDYbOnDkj8fHxMmHChCy3mzNnjqxdu9YETQAAAHmmmaxjx45mycqBAwdk4MCBsmjRIrntttsuuc/U1FSzOKWkpASlrAAA2EUUzWThw+FwyAMPPCDDhw+X2rVr+/SYpKQkKV68uGuJi4vL8XICAJAne5NZAS4RIqyDoTFjxkiBAgVk0KBBPj8mMTFRTp065VqSk5NztIwAACCyhW1vsg0bNsgbb7whGzduNInTvoqOjjYLAADIniiaycLDypUr5ejRo1K5cmVTO6TLvn375LHHHpOqVauGungAAORdlr16k4VtzZDmCrVt29ZjXfv27c363r17h6xcAAAgbwlpMHT69GnZtWuX6/bevXtl8+bNUqpUKVMjVLp0aY/tCxYsKLGxsXLNNdeEoLQAANhDlM2ayUIaDK1fv15at27tuj1s2DDzNyEhQaZPnx7CkgEAYGOWveYmC2kw1KpVK7H8aFP87bffcrQ8AADAfsI2ZwgAAIRGFM1kAADA1hzWf5dA9xEhwrZrPQAAQG6gZggAANg6gZqaIQAAYGvUDAEAAA86CVbACdQSOQiGAACAp2BMpxFB03HQTAYAAGyNYAgAAHgdZyjQJTsmTJhgJmQvXLiwNGvWTNatW5fptu+++67ceOONUrJkSbPonKZZbZ8ZgiEAAOC9N1mgi59mz55tpuYaNWqUbNy4UeLj480k7UePHvW6/bJly6R79+6ydOlSWbNmjcTFxUm7du3kwIEDfj0vwRAAAAgL48aNk379+knv3r2lVq1aMmnSJClatKhMnTrV6/Yff/yxPProo1K/fn2pWbOmvPfee+JwOGTJkiV+PS/BEAAA8BBlWUFZVEpKiseSmpoq3pw/f142bNhgmrqc8uXLZ25rrY8vzp49KxcuXJBSpUr5tL3refzaGgAA5H2OIC0ipumqePHiriUpKcnrUx4/flzS0tKkfPnyHuv19uHDh30q9ogRI6RixYoeAZUv6FoPAAByTHJyssTExLhuR0dH58jzvPzyyzJr1iyTR6TJ1/4gGAIAAB7cm7myy/l4DYTcg6HMlClTRvLnzy9HjhzxWK+3Y2Njs3zsq6++aoKh7777TurVq+d3WWkmAwAAIe9NVqhQIWnUqJFH8rMzGbp58+aZPm7s2LHy/PPPy8KFC6Vx48aSHdQMAQCAsKDd6hMSEkxQ07RpUxk/frycOXPG9C5TPXv2lEqVKrnyjsaMGSMjR46UGTNmmLGJnLlFxYoVM4uvCIYAAEBYTMfRrVs3OXbsmAlwNLDRLvNa4+NMqt6/f7/pYeY0ceJE0wvtnnvu8diPjlM0evRon5+XYAgAAHgIZARp931kx4ABA8zijSZHu/vtt98kGMgZAgAAtkbNEAAAsPWs9QRDAADAQ5Tjv0sgAn18bqKZDAAA2Bo1QwAAwBPNZAAAwNYs/wdN9LqPCEEzGQAAsDVqhgAAQI7NTRYJQloztGLFCunUqZNUrFhRoqKiZO7cuR736+iRNWvWlMsuu0xKliwpbdu2lR9++CFk5QUAwFY5Q1aAS4QIaTCk843Ex8fLhAkTvN5fo0YNeeutt2TLli2yatUqM+9Iu3btzFDdAAAAEd9M1rFjR7Nk5r777vO4PW7cOJkyZYr89NNP0qZNm1woIQAANmTplPFB2EeEiJicIZ2IbfLkyVK8eHFTm5SZ1NRUszilpKTkUgkBAMgbosgZCi8LFiyQYsWKSeHCheX111+XxYsXS5kyZTLdPikpyQRMziUuLi5XywsAACJL2AdDrVu3ls2bN8vq1aulQ4cO0rVrVzl69Gim2ycmJsqpU6dcS3Jycq6WFwCAvDHOkBXgIhEj7IMh7Ul21VVXyXXXXWfyhQoUKGD+ZiY6OlpiYmI8FgAA4AeL3mRhzeFweOQEAQAARGwC9enTp2XXrl2u23v37jVNYqVKlZLSpUvLiy++KLfffrtUqFBBjh8/brrgHzhwQLp06RLKYgMAkLc5NAM6CPuIECENhtavX29ygpyGDRtm/iYkJMikSZNk+/bt8v7775tASIOjJk2ayMqVK6V27dohLDUAAHlblM16k4U0GGrVqpVYWRysL774IlfLAwAA7CdixhkCAAC5xApCAjQ1QwAAIGJZ9gqGIq43GQAAQDBRMwQAAGxdM0QwBAAAbN21nmYyAABga9QMAQAAD4wzBAAA7M2yV84QzWQAAMDWqBkCAACeHJa2c0nA+4gQBEMAAMATzWQAAAD2Qc0QAABIJwg1Q7qPCEEwBAAAPNFMBgAAYB/UDAEAAC89wehNBgAA7Mpy/HcJdB8RgmYyAABga9QMAQAAWydQEwwBAABb5wzRTAYAAGyNmiEAAOCJZjIAAGBrVhCCmciJhWgmAwAA9kbNEAAA8EQzGQAAsDWHDpjoCMI+IgPNZAAAwNaoGQIAALZuJgtpzdCKFSukU6dOUrFiRYmKipK5c+e67rtw4YKMGDFC6tatK5dddpnZpmfPnnLw4MFQFhkAAPsEQ1aAS4QIaTB05swZiY+PlwkTJmS47+zZs7Jx40Z55plnzN8vvvhCduzYIbfffntIygoAAPKmkDaTdezY0SzeFC9eXBYvXuyx7q233pKmTZvK/v37pXLlyl4fl5qaahanlJSUIJcaAIA8zsF0HGHr1KlTpjmtRIkSmW6TlJRkAinnEhcXl6tlBAAg0lmWIyhLpIiYYOjcuXMmh6h79+4SExOT6XaJiYkmaHIuycnJuVpOAAAQWSKiN5kmU3ft2lUsy5KJEydmuW10dLRZAABANllW4M1cEZRAXSBSAqF9+/bJ999/n2WtEAAACAIrCDlDBEPBDYR+/fVXWbp0qZQuXTrURQIAAHlMSIOh06dPy65du1y39+7dK5s3b5ZSpUpJhQoV5J577jHd6hcsWCBpaWly+PBhs53eX6hQoRCWHACAPMzhEIkKMAE6ghKoQxoMrV+/Xlq3bu26PWzYMPM3ISFBRo8eLfPnzze369ev7/E4rSVq1apVLpcWAACbsGgmyzUa0GhSdGayug8AACDP5wwBAIDcZzkcYgXYTBZJ4wwRDAEAAFs3k0XMoIsAAAA5gZohAADgSQdcjLJPzRDBEAAA8BLIOGwTDNFMBgAAbI2aIQAA4MFyWGIF2EwWScPjEAwBAABPplu8fUagppkMAACEjQkTJkjVqlWlcOHC0qxZM1m3bl2W23/66adSs2ZNs33dunXl66+/9vs5CYYAAEDGZrIgLP6aPXu2mZpr1KhRZm7S+Ph4ad++vRw9etTr9qtXr5bu3bvLgw8+KJs2bZLOnTubZevWrX49b5QVSY162ZCSkiLFixeXEzurSczlxH4AgMiS8pdDStbYI6dOnZKYmJhcuWa2kjukQFTBgPZ10bogy2SeX+XWmqAmTZrIW2+9ZW47HA6Ji4uTgQMHyhNPPJFh+27dusmZM2fMhO5O1113nZnTdNKkST6XNc/nDDljvZTTkdN2CQCAk/P6lZt1FxflQsADUJt9/C/AchcdHW2W9M6fPy8bNmyQxMRE17p8+fJJ27ZtZc2aNV6fQ9c7J3l30pqkuXPn+lXWPB8M/fXXX+ZvlYa/hbooAAAEdD3TWpucVKhQIYmNjZVVh/3Pu/GmWLFipmbHnTaBjR49OsO2x48fl7S0NClfvrzHer29fft2r/s/fPiw1+11vT/yfDBUsWJFSU5Olssvv1yioqKCtl+NdPUN1n3ndLWlncoaaeWlrDknksobSWWNtPJS1v/WCGkgpNeznFa4cGHZu3evqaUJVtnTX3u91QqFWp4PhrSK7Yorrsix/esJH+4f0Egsa6SVl7LmnEgqbySVNdLKa/ey5nSNUPqASJfcVqZMGcmfP78cOXLEY73e1toqb3S9P9tnhoxiAAAQctpE16hRI1myZIlrnSZQ6+3mzZt7fYyud99eLV68ONPtbVszBAAAIsOwYcMkISFBGjduLE2bNpXx48eb3mK9e/c29/fs2VMqVaokSUlJ5vbgwYOlZcuW8tprr8ltt90ms2bNkvXr18vkyZP9el6CoWzSNk9NAgvHts9ILmuklZey5pxIKm8klTXSyktZ7aVbt25y7NgxGTlypEmC1i7yCxcudCVJ79+/36S/OF1//fUyY8YMefrpp+XJJ5+Uq6++2vQkq1Onjl/Pm+fHGQIAAMgKOUMAAMDWCIYAAICtEQwBAABbIxgCAAC2RjDkpxUrVkinTp3MSKA6qqa/85/kJu16qBPe6ejb5cqVMzP57tixQ8LRxIkTpV69eq7BynSMiG+++UYiwcsvv2zOhSFDhkg40mHvtXzuS82aNSVcHThwQO6//34pXbq0FClSROrWrWu6yoajqlWrZji2uvTv31/CjU5z8Mwzz8iVV15pjmv16tXl+eefz9X5rvyhIy7rZ6pKlSqmvNpr6Mcff5RIuA7oMdXeUBUqVDBl17m1fv3115CVF5dGMOQnHe8gPj5eJkyYIOFu+fLl5kt57dq1ZhCqCxcuSLt27cxrCDc6SrgGFTpJn174br75Zrnjjjvk559/lnCmX87vvPOOCeTCWe3ateXQoUOuZdWqVRKOTpw4IS1atJCCBQuaYPiXX34x44eULFlSwvX9dz+u+jlTXbp0kXAzZswY86NDZwPftm2buT127Fh58803JRz17dvXHM8PP/xQtmzZYr67NKjQYDncrwN6XP/1r3+ZWdN/+OEHueyyy8zkoefOncv1ssJH2rUe2aOHb86cOVakOHr0qCnz8uXLrUhQsmRJ67333rPC1V9//WVdffXV1uLFi62WLVtagwcPtsLRqFGjrPj4eCsSjBgxwrrhhhusSKXnQPXq1S2Hw2GFm9tuu83q06ePx7q77rrL6tGjhxVuzp49a+XPn99asGCBx/qGDRtaTz31lBXO1wF972NjY61XXnnFte7kyZNWdHS0NXPmzBCVEpdCzZCNnDp1yvwtVaqUhDOtztdRRPXXl79DqucmrXXTEU/112q40yp6rdKvVq2a9OjRwwxcFo7mz59vRp7VmhVt2m3QoIG8++67Egl0YsuPPvpI+vTpE9RJoYNFm5l02oKdO3ea2//5z39MDWHHjh0l3Fy8eNF8D6SfH0ubnMK1VtNJJznVwQLdvxd0XrFmzZrJmjVrQlo2ZI4RqG1C53fR9ndtgvB3ZM7colXhGvxoVXKxYsVkzpw5UqtWLQlHGqxt3LgxbHIYsqJfwtOnT5drrrnGNOU8++yzcuONN8rWrVtNPlk42bNnj2nK0SH5dTRZPb6DBg0ycxbpEP3hTPNGTp48Kb169ZJw9MQTT5hZ1TVfTCfD1GDjxRdfNMFxuNHzUr8LNKfp2muvNaMPz5w50wQTV111lYQzDYSUc8RkJ73tvA/hh2DIJrQWQy9+4fyrSi/WmzdvNjVYn332mbn4ad5TuAVEycnJZj4czWcIxczO/nL/5a+5TRocaVLqJ598Ig8++KCEW9CuNUMvvfSSua01Q3reau5FuAdDU6ZMMcdaa+DCkb7fH3/8sZm6QHPI9LOmP5C0vOF4bDVXSGvZdB4qDd4aNmwo3bt3N3mFQLDRTGYDAwYMkAULFsjSpUtNonK40l//+qtPZy3WnnCaoPjGG29IuNEv46NHj5ov5wIFCphFgzZNmNR/6y/ucFaiRAmpUaOG7Nq1S8KN9r5JH/xqzUC4Nus57du3T7777juT9Buuhg8fbmqH7r33XtND74EHHpChQ4e6JrwMN9rbTT9Xp0+fNj9A1q1bZzqBaFNvOIuNjTV/jxw54rFebzvvQ/ghGMrDNLdPAyFtbvr+++9Nl9pIorUEqampEm7atGljmvT0l7Vz0doMbW7Qf+uv2HCmF5fdu3ebwCPcaDNu+uEfNMdFa7LC2bRp00yOk+aQhauzZ896THCp9FzVz1k4055Yeq5qT8NFixaZXqbhTL9nNejR/CwnbZ7UXmXhnANpdzSTZeNC4v6LWpPl9AKoScmVK1eWcGsa0yrxefPmmTZ4Z3u1JvNpImI4SUxMNE0Megx1fBEt97Jly8yXX7jRY5k+70q/sHVcnHDMx/rnP/9pxkTRgOLgwYNmVm29CGqTQ7jRmgpN9NVmsq5du5ragMmTJ5slXGkwocGQNjVpzWC40nNAc4T0M6bNZJs2bZJx48aZpqhwpJ99/UGnzef6nas1W5rv1Lt377C/Dmjz4wsvvGBmUNfgSMd30uZIHesNYeqS/c3gYenSpaYrZfolISHBCjfeyqnLtGnTrHCjXX6rVKliFSpUyCpbtqzVpk0b69tvv7UiRTh3re/WrZtVoUIFc2wrVapkbu/atcsKV19++aVVp04d0xW5Zs2a1uTJk61wtmjRIvO52rFjhxXOUlJSzDlauXJlq3Dhwla1atVMN/XU1FQrHM2ePduUUc9b7arev39/00U9Eq4D2r3+mWeescqXL2/OY/0+C/fzw+6i9H+hDsgAAABChZwhAABgawRDAADA1giGAACArREMAQAAWyMYAgAAtkYwBAAAbI1gCAAA2BrBEAAAsDWCISDCVK1aVcaPH5+rz6lTo0RFRcnJkydz7Tl79eqVa9MX/PHHH2Zusd9++83nY7Bw4UKpX79+2M/tBeDSCIaAIFy09SKpS8GCBaV8+fJyyy23yNSpU7lQBuCNN96Q6dOn58pz6ZxdOgGoBpq+6tChg3m/P/744xwtG4CcRzAEBIFeGA8dOmRqFr755htp3bq1DB48WP7xj3/IxYsXJZycP39eIoFOKFyiRIlcmc19ypQp8uCDD2YrEP7Xv/6VI+UCkHsIhoAgiI6OltjYWKlUqZI0bNhQnnzySZk3b54JjNxrN7SJpW/fvlK2bFmJiYmRm2++Wf7zn/+47t+9e7epodDapWLFikmTJk3ku+++y/K5L7XP0aNHm+ac9957z8ygXbhwYa/72bdvn5nZvGTJknLZZZeZmc2//vprj202bNggjRs3lqJFi5rZ5Xfs2OFx/8SJE6V69epSqFAhM9v4hx9+6Lrvn//8pwkOnbSpT2vTtLnJ6aqrrjLl9NZM1qpVKxk0aJA8/vjjZnZwPd762txt375dbrjhBvMaa9WqZY6dPsfcuXMzPX76GvX9u+666zKsr1GjhhQpUsQEt96a0PR4rV+/3rxvACIXwRCQQzQoiY+Ply+++MK1rkuXLnL06FETJGlgoYFTmzZt5M8//zT3nz59Wm699VZZsmSJbNq0ydQ46QV3//79mT7Ppfapdu3aJZ9//rkpy+bNm73up3///pKamiorVqyQLVu2yJgxY0xA5u6pp56S1157zQQABQoUkD59+rjumzNnjqkNe+yxx2Tr1q3yf//3f9K7d29ZunSpub9ly5ayatUqSUtLM7eXL18uZcqUMbk46sCBAyao0KAnM++//74J1H744QcZO3asPPfcc7J48WJzn+5XgycN1PT+yZMnm/JeysqVK6VRo0Ye65KTk+Wuu+4yx16PlwabTzzxRIbHVq5c2QSuug8AESzwie8Be0tISLDuuOMOr/d169bNuvbaa82/V65cacXExFjnzp3z2KZ69erWO++8k+n+a9eubb355puu21WqVLFef/11n/c5atQoq2DBgtbRo0ezfB1169a1Ro8e7fW+pUuXWvp18d1337nWffXVV2bd33//bW5ff/31Vr9+/Twe16VLF+vWW281/z5x4oSVL18+68cff7QcDodVqlQpKykpyWrWrJm5/6OPPrIqVaqU6XFt2bKldcMNN3jsv0mTJtaIESPMv7/55hurQIEC1qFDh1z3L1682JRxzpw5mb5ufY4+ffp4rEtMTLRq1arlsU6fR/elr8NdgwYNMj1uACIDNUNADrIsyzTTKG260pqf0qVLmxoX57J3715XM4ver81J1157rcmX0fu3bduWac2QL/tUVapUMc1oWdEmqBdeeEFatGgho0aNkp9++inDNvXq1XP9u0KFCuav1kopLac+1p3e1vVKX4/WlGlNkNY8aVPaQw89ZGrA9DVoTZHWHmXF/fmdZXA+vzbZxcXFmeYzp6ZNm8ql/P333xmaDrXMzZo181jXvHlzr4/XZjTNOwIQuQqEugBAXqYXVc3TUXrB14u3s1nInTNRWAMhbfZ59dVXTf6MXmjvueeeTJOefdmn0qalS9GmoPbt28tXX30l3377rSQlJZkmsYEDB7q20d5TTs4gz58ec9oEpmXVHB0NfDT3RwM/bT7TYEib2LLi/vzOMgTaY0+b6k6cOJHtx2tz5KUCTQDhjZohIId8//33pgbk7rvvNrc1l+fw4cMm10YDHfdFL8jq3//+t0kcvvPOO6Vu3bqmliOrsW982ac/tGbl4YcfNrlFGpi8++67Pj9Wgxotvzu9rYnMTs68Ic2JcuYG6d+ZM2fKzp07s8wXuhRN2NZcnyNHjrjW/fjjj5d8XIMGDeSXX37J8FrWrVvnsW7t2rUZHnvu3DlTA6f7ABC5CIaAINDEYw1KNAl448aN8tJLL5leYdp7qmfPnmabtm3bmqYWTfLVmhcNclavXm2SfDUhWV199dWuJGdtArvvvvuyrPnwZZ++GjJkiCxatMg0selr0MRnDQp8NXz4cNNzTnuU/frrrzJu3DjzWrS2y+mmm26Sv/76SxYsWOARDOlYPVrDpb23skvHdtKebAkJCaaJTwOxp59+2qMWyxutDfv55589aoc0INTXoK9Jm99mzJjhdcwjDZC0liuzJjQAkYFgCAgC7R6uF3MdtE97gGkgoePPaPf6/Pnzuy7I2l1bAwLtZaUX/nvvvdd0adceSUoDCO3art3WtSeTXqi19iczvuzTV9obS3uUaQCkr0H39fbbb/v8eA3IdKBEbeLTbvnvvPOOTJs2zaO2R1+b1nhps1LNmjXNOi27BnyXyhe6FD3O2oVemw51SAJt9nP2JstsOAGl5dFj/Mknn3j0EtPed7o/zXOaNGmSCXDT0xqtHj16mB5sACJXlGZRh7oQAJATtHZIxx3SoQW01igzmieltUA6JEC+fL79Rjx+/LhpmtMaOGdeGIDIRAI1gDxDxzrS3nTa3KgBkI57pD3asgqE1G233WaaxbSZU/OmfKFNklpzRiAERD5qhgDkGR988IEZHkCHItAEcs2p0h5xOvQAAGSGYAgAANgaCdQAAMDWCIYAAICtEQwBAABbIxgCAAC2RjAEAABsjWAIAADYGsEQAACwNYIhAAAgdvb/XAzR4PXYQRgAAAAASUVORK5CYII=",
"text/plain": [
"<Figure size 700x500 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 700x500 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 700x500 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"for usable in [0, 1]:\n",
" for name, pi in policies.items():\n",
" grid_pi = to_grid_from_policy(pi, usable)\n",
" plot_policy_map(grid_pi, title=f\"{name} — policy map (usable_ace={usable})\")\n"
]
},
{
"cell_type": "markdown",
"id": "cd81c661-dfe9-4a53-95fe-189846907656",
"metadata": {},
"source": [
"We now perform a **quantitative comparison** of the greedy policies\n",
"learned by the different Monte Carlo control methods.\n",
"\n",
"For two policies $\\pi_1$ and $\\pi_2$, we define the **policy agreement rate** as the\n",
"fraction of states in which both policies choose the **same action**:\n",
"$$\n",
"\\text{Agreement}(\\pi_1,\\pi_2)\n",
"= \\frac{1}{|\\mathcal S|}\n",
"\\sum_{s \\in \\mathcal S}\n",
"\\mathbf{1}\\{\\pi_1(s) = \\pi_2(s)\\}.\n",
"$$\n",
"\n",
"The state space considered here includes all Blackjack states with:\n",
"- player sums $p = 12,\\dots,21$,\n",
"- dealer showing cards $d = 1,\\dots,10$,\n",
"- both cases of usable ace ($u \\in \\{0,1\\}$).\n",
"\n",
"An agreement rate close to **1** indicates that two methods have learned **very similar policies**,\n",
"while lower values reveal systematic differences in decision-making.\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 253,
"id": "e6d2c364-d042-42f4-a0ed-ec48b20f9c24",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Agreement Exploring Starts vs On-policy ε-soft: 0.970\n",
"Agreement Exploring Starts vs Off-policy IS: 0.970\n",
"Agreement On-policy ε-soft vs Off-policy IS: 0.980\n"
]
}
],
"source": [
"def policy_agreement(pi_a: dict, pi_b: dict) -> float:\n",
" \"\"\"Compute agreement rate between two policies over all states.\n",
"\n",
" Args:\n",
" pi_a: first policy dict mapping state -> action\n",
" pi_b: second policy dict mapping state -> action\n",
"\n",
" Returns:\n",
" agreement_rate: float in [0, 1] representing the fraction of states\n",
" where both policies agree on the action.\n",
"\n",
" \"\"\"\n",
" states = [(p, d, u) for u in [0, 1] for p in range(12, 22) for d in range(1, 11)]\n",
" agree = 0\n",
" for s in states:\n",
" a = pi_a.get(s, HIT)\n",
" b = pi_b.get(s, HIT)\n",
" agree += int(a == b)\n",
" return agree / len(states)\n",
"\n",
"\n",
"names = list(policies.keys())\n",
"for i in range(len(names)):\n",
" for j in range(i + 1, len(names)):\n",
" a, b = names[i], names[j]\n",
" print(f\"Agreement {a} vs {b}: {policy_agreement(policies[a], policies[b]):.3f}\")\n"
]
},
{
"cell_type": "markdown",
"id": "f4f6ea4b-b3bf-4560-af0c-abd9d6f866c6",
"metadata": {},
"source": [
"**Evaluating the Value Function of the Learned Policies**\n",
"\n",
"The Monte Carlo control algorithms studied so far directly estimate **action-value functions**\n",
"$Q(s,a)$ and output a **greedy policy** $\\hat{\\pi}$.\n",
"However, to compare the *quality* of these learned policies, we must evaluate **how good each policy actually is**.\n",
"\n",
"To do this, we perform **Monte Carlo policy evaluation** for each learned policy $\\hat{\\pi}$.\n",
"More precisely, for a fixed policy $\\pi$, we estimate its **state-value function**:\n",
"$$\n",
"V^{\\pi}(s) = \\mathbb{E}_{\\pi}[G \\mid S_0 = s],\n",
"$$\n",
"where \\( G \\) denotes the terminal return of a Blackjack episode.\n",
"\n",
"We use **first-visit Monte Carlo evaluation** (cf. Exercise 2. but here with another input which is the policy).\n"
]
},
{
"cell_type": "code",
"execution_count": 254,
"id": "ba15bc9c-a5ba-4241-a206-8cbe2bf63811",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 700x500 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 700x500 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 700x500 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 700x500 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 700x500 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 700x500 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def mc_policy_evaluation_V(\n",
" policy: dict, num_episodes: int = 200_000, rng: np.random.Generator = rng,\n",
") -> dict:\n",
" \"\"\"First-visit Monte Carlo policy evaluation that estimates V^pi(s) for all visited states s.\n",
"\n",
" Args:\n",
" policy: dict mapping state -> action\n",
" num_episodes: number of episodes to sample\n",
" rng: random generator used to draw cards\n",
"\n",
" Returns:\n",
" V: dict mapping state -> estimated value\n",
"\n",
" \"\"\"\n",
" if rng is None:\n",
" rng = np.random.default_rng(123)\n",
"\n",
" returns_sum = defaultdict(float)\n",
" returns_count = defaultdict(int)\n",
"\n",
" def pi(s: tuple[int, int, int]) -> int:\n",
" \"\"\"Policy function using the provided policy dict.\"\"\"\n",
" return policy.get(s, HIT)\n",
"\n",
" for _ in range(num_episodes):\n",
" episode, G = generate_episode(pi, rng)\n",
" visited = set()\n",
"\n",
" for s, _a in episode:\n",
" p, _d, _u = s\n",
" if p < 12: # noqa: PLR2004\n",
" continue\n",
"\n",
" if s not in visited:\n",
" visited.add(s)\n",
" returns_sum[s] += G\n",
" returns_count[s] += 1\n",
"\n",
" return {s: returns_sum[s] / returns_count[s] for s in returns_sum}\n",
"\n",
"\n",
"rng_eval = np.random.default_rng(999)\n",
"\n",
"V_of_policy = {}\n",
"for name, pi in policies.items():\n",
" V_of_policy[name] = mc_policy_evaluation_V(pi, num_episodes=300_000, rng=rng_eval)\n",
"\n",
"for usable in [0, 1]:\n",
" for name, V in V_of_policy.items():\n",
" grid_V = to_grid_from_V(V, usable) # noqa: N816\n",
" plot_value_heatmap(grid_V, title=f\"{name} — V^π (usable_ace={usable})\")\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "469c4300-5fa1-4b2d-bb7d-3da032a1e147",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"id": "9c0d7e8a-64a0-4fa3-adbb-65e723900d20",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "studies",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.13.9"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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