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ArtStudies/M2/Reinforcement Learning/Lab 2 - Second maze.ipynb

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{
"cells": [
{
"cell_type": "markdown",
"id": "44b75d44",
"metadata": {},
"source": [
"# Lab 2 - Second maze\n",
"\n",
"\n",
"\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 535,
"id": "100d1e0d",
"metadata": {},
"outputs": [],
"source": [
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"\n",
"np.set_printoptions(\n",
" precision=3, suppress=True\n",
") # (not mandatory) This line is for limiting floats to 3 decimal places, avoiding scientific notation (like 1.23e-04) for small numbers.\n",
"\n",
"# For reproducibility\n",
"rng = np.random.default_rng(seed=42) # This line creates a random number generator.\n"
]
},
{
"cell_type": "markdown",
"id": "1018deab",
"metadata": {},
"source": [
"## 2. Maze definition and MDP formulation\n"
]
},
{
"cell_type": "markdown",
"id": "ca4fa301-c14f-44ec-b04f-b01ca42d979a",
"metadata": {},
"source": [
"### 2.1 Define the maze "
]
},
{
"cell_type": "code",
"execution_count": 536,
"id": "f91cda05",
"metadata": {},
"outputs": [],
"source": [
"maze_str = [\n",
" \"############\",\n",
" \"#S#.......X#\",\n",
" \"#.#.###.#.##\",\n",
" \"#.....#X#..#\",\n",
" \"#.###.####.#\",\n",
" \"#...#X#X...#\",\n",
" \"###.######X#\",\n",
" \"#.....X...##\",\n",
" \"#.###.#.#..#\",\n",
" \"#...#...X#.#\",\n",
" \"#X#.X#X##G.#\",\n",
" \"############\",\n",
"]"
]
},
{
"cell_type": "code",
"execution_count": 537,
"id": "564cb757-eefe-4be6-9b6f-bb77ace42a97",
"metadata": {},
"outputs": [],
"source": [
"n_rows = len(maze_str)\n",
"n_cols = len(maze_str[0])\n",
"\n",
"figsize = (n_cols / 2 if n_cols > n_rows else 8, n_rows / 2 if n_rows > n_cols else 8)"
]
},
{
"cell_type": "markdown",
"id": "adc49d58-2730-41d8-96fb-ca7c9cb4fcdf",
"metadata": {},
"source": [
"### 2.2 Map each walkable cell (not a wall '#') to a state index\n"
]
},
{
"cell_type": "code",
"execution_count": 538,
"id": "7116044b-c134-43de-9f30-01ab62325300",
"metadata": {},
"outputs": [],
"source": [
"FREE = {\n",
" \".\",\n",
" \"S\",\n",
" \"G\",\n",
" \"X\",\n",
"} # The vector Free represents cells that the agent is allowed to move into.\n"
]
},
{
"cell_type": "markdown",
"id": "1c9ad05e-9c6c-4e00-918c-44b858f45298",
"metadata": {},
"source": [
"**Dictionaries to convert between grid and state index**"
]
},
{
"cell_type": "code",
"execution_count": 539,
"id": "a1258de4",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Number of states (non-wall cells): 62\n",
"Start state: 0 at (1, 1)\n",
"Goal states: [60] at (10, 9)\n",
"Trap states: [8, 18, 27, 28, 33, 39, 54, 56, 58, 59] at (1, 10)\n"
]
}
],
"source": [
"state_to_pos = {} # s -> (i,j)\n",
"pos_to_state = {} # (i,j) -> s\n",
"\n",
"start_state = None # will store the state index of start state\n",
"goal_states = [] # will store the state index of goal state # We use a list in case there are multiple goals\n",
"trap_states = [] # will store the state index of trap state # We use a list in case there are multiple traps\n",
"\n",
"s = 0\n",
"for i in range(n_rows): # i = row index\n",
" for j in range(n_cols): # j = column index\n",
" cell = maze_str[i][j] # cell = the character at that position (S, ., #, etc.)\n",
"\n",
" if (\n",
" cell in FREE\n",
" ): # FREE contains: free cells \".\", start cell \"S\", goal cell \"G\" and trap cell \"X\"\n",
" # Walls # are ignored, they are not MDP states.\n",
" state_to_pos[s] = (i, j)\n",
" pos_to_state[(i, j)] = s\n",
"\n",
" if cell == \"S\":\n",
" start_state = s\n",
" elif cell == \"G\":\n",
" goal_states.append(s)\n",
" elif cell == \"X\":\n",
" trap_states.append(s)\n",
"\n",
" s += 1\n",
"\n",
"n_states = s\n",
"\n",
"print(\"Number of states (non-wall cells):\", n_states)\n",
"print(\"Start state:\", start_state, \"at\", state_to_pos[start_state])\n",
"print(\"Goal states:\", goal_states, \"at\", state_to_pos[goal_states[0]])\n",
"print(\"Trap states:\", trap_states, \"at\", state_to_pos[trap_states[0]])\n"
]
},
{
"cell_type": "code",
"execution_count": 540,
"id": "fc61ceef-217c-47f4-8eba-0353369210db",
"metadata": {},
"outputs": [
{
"data": {
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",
"text/plain": [
"<Figure size 800x800 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def plot_maze_with_states():\n",
" \"\"\"Plot the maze with state indices.\"\"\"\n",
" grid = np.ones(\n",
" (n_rows, n_cols)\n",
" ) # Start with a matrix of ones. Here 1 means “free cell”\n",
" for i in range(n_rows):\n",
" for j in range(n_cols):\n",
" if maze_str[i][j] == \"#\":\n",
" grid[i, j] = 0 # We replace walls (#) with 0\n",
"\n",
" fig, ax = plt.subplots(figsize=figsize)\n",
" ax.imshow(grid, cmap=\"gray\", alpha=0.7)\n",
"\n",
" # Plot state indices\n",
" for (\n",
" s,\n",
" (i, j),\n",
" ) in state_to_pos.items(): # Calling .items() returns a list-like sequence of (key, value) pairs in the dictionary.\n",
" cell = maze_str[i][j]\n",
"\n",
" if cell == \"S\":\n",
" label = f\"S\\n{s}\"\n",
" color = \"green\"\n",
" elif cell == \"G\":\n",
" label = f\"G\\n{s}\"\n",
" color = \"blue\"\n",
" elif cell == \"X\":\n",
" label = f\"X\\n{s}\"\n",
" color = \"red\"\n",
" else:\n",
" label = str(s)\n",
" color = \"black\"\n",
"\n",
" ax.text(\n",
" j,\n",
" i,\n",
" label, # Attention : matplotlib, text(x, y, ...) expects (column, row)\n",
" ha=\"center\",\n",
" va=\"center\",\n",
" fontsize=10,\n",
" fontweight=\"bold\",\n",
" color=color,\n",
" )\n",
"\n",
" ax.set_xticks([]) # remove numeric axes, we don't need.\n",
" ax.set_yticks([])\n",
" ax.set_title(\"Maze with state indices\")\n",
"\n",
" plt.show()\n",
"\n",
"\n",
"plot_maze_with_states()"
]
},
{
"cell_type": "markdown",
"id": "db078d86",
"metadata": {},
"source": [
"### 2.4 Actions and deterministic movement"
]
},
{
"cell_type": "code",
"execution_count": 541,
"id": "f7f0b8e4-1f48-4d03-9e5f-a47e59c3e827",
"metadata": {},
"outputs": [],
"source": [
"A_UP, A_RIGHT, A_DOWN, A_LEFT = 0, 1, 2, 3\n",
"ACTIONS = [A_UP, A_RIGHT, A_DOWN, A_LEFT]\n",
"action_names = {A_UP: \"\\u2191\", A_RIGHT: \"\\u2192\", A_DOWN: \"\\u2193\", A_LEFT: \"\\u2190\"}"
]
},
{
"cell_type": "code",
"execution_count": 542,
"id": "4b06da5e-bc63-48e5-a336-37bce952443d",
"metadata": {},
"outputs": [],
"source": [
"def move_deterministic(i: int, j: int, a: int) -> tuple[int, int]:\n",
" \"\"\"Deterministic movement on the grid. If the movement hits a wall or boundary, the agent stays in place.\n",
"\n",
" Args:\n",
" i (int): current row index\n",
" j (int): current column index\n",
" a (int): action to take (A_UP, A_DOWN, A_LEFT, A_RIGHT)\n",
"\n",
" Returns:\n",
" (tuple[int, int]): new (row, column) position after taking action a\n",
"\n",
" \"\"\"\n",
" candidate_i, candidate_j = (\n",
" i,\n",
" j,\n",
" ) # It means “Unless the action succeeds, the robot stays in place.”\n",
"\n",
" # Now each action changes the coordinates of the robot:\n",
" if a == A_UP:\n",
" candidate_i, candidate_j = (\n",
" i - 1,\n",
" j,\n",
" ) # if the action is UP, then row becomes row -1\n",
" elif a == A_DOWN:\n",
" candidate_i, candidate_j = (\n",
" i + 1,\n",
" j,\n",
" ) # if the action is DOWN, then row becomes row +1\n",
" elif a == A_LEFT:\n",
" candidate_i, candidate_j = (\n",
" i,\n",
" j - 1,\n",
" ) # if the action is LEFT, then column becomes column -1\n",
" elif a == A_RIGHT:\n",
" candidate_i, candidate_j = (\n",
" i,\n",
" j + 1,\n",
" ) # if the action is RIGHT, then column becomes column +1\n",
"\n",
" # Check boundaries\n",
" if not (0 <= candidate_i < n_rows and 0 <= candidate_j < n_cols):\n",
" # If the robot tries to move outside the maze\n",
" # It will not move and it stays at (i, j).\n",
" return i, j\n",
"\n",
" # Check wall\n",
" if maze_str[candidate_i][candidate_j] == \"#\":\n",
" # If the next cell is a wall, the robot stays in place.\n",
" return i, j\n",
"\n",
" return candidate_i, candidate_j # Otherwise, return the new position\n"
]
},
{
"cell_type": "markdown",
"id": "c9e620e6",
"metadata": {},
"source": [
"### 2.5 Transition probabilities and reward function"
]
},
{
"cell_type": "code",
"execution_count": 543,
"id": "610253e7-f3f7-4a30-be3e-2ec5a1e2ed04",
"metadata": {},
"outputs": [],
"source": [
"gamma = 0.95\n",
"p_error = 0.1 # probability of the error to a random other direction\n"
]
},
{
"cell_type": "code",
"execution_count": 544,
"id": "7a51f242-fe4e-4e74-8a1f-a8df32b194b8",
"metadata": {},
"outputs": [],
"source": [
"# Initialize transition matrices and reward vector\n",
"P = np.zeros((len(ACTIONS), n_states, n_states))\n",
"R = np.zeros(n_states)"
]
},
{
"cell_type": "code",
"execution_count": 545,
"id": "49d54d1f-dc29-45b6-ad31-ad0e848f920d",
"metadata": {},
"outputs": [],
"source": [
"# Set rewards for each state\n",
"step_penalty = -0.01\n",
"goal_reward = 1.0\n",
"trap_reward = -1.0\n"
]
},
{
"cell_type": "code",
"execution_count": 546,
"id": "b9b7495a-c233-425c-99c0-5bddaf6c3225",
"metadata": {},
"outputs": [],
"source": [
"for s in range(n_states):\n",
" if s in goal_states:\n",
" R[s] = goal_reward\n",
" elif s in trap_states:\n",
" R[s] = trap_reward\n",
" else:\n",
" R[s] = step_penalty\n"
]
},
{
"cell_type": "code",
"execution_count": 547,
"id": "eca4c571-39c7-468b-af86-0bab9489415e",
"metadata": {},
"outputs": [],
"source": [
"terminal_states = set(goal_states + trap_states)\n",
"\n",
"\n",
"def is_terminal(s: int) -> bool:\n",
" \"\"\"Check if a state is terminal (goal or trap).\"\"\"\n",
" return s in terminal_states\n"
]
},
{
"cell_type": "code",
"execution_count": 548,
"id": "2d03276b-e206-4d1f-9024-f6948ca61523",
"metadata": {},
"outputs": [],
"source": [
"for s in range(n_states): # We loop over all states s.\n",
" i, j = state_to_pos[\n",
" s\n",
" ] # We recover the states to their coordinates (i, j) in the maze.\n",
"\n",
" # First, in a goal or trap state,\n",
" # No matter which action you “choose”, you stay in the same state with probability 1.\n",
" # This makes the terminal states as the absorbing states.\n",
" if is_terminal(s):\n",
" # Terminal states: stay forever\n",
" for a in ACTIONS:\n",
" P[a, s, s] = goal_reward\n",
" continue\n",
"\n",
" # If the state is non-terminal, we define the stochastic movement.\n",
" # For a given state s and intended action a,\n",
" # With probability 1 - p_error, the robot will move in direction a;\n",
" # With probability p_error, the robot will move in one of the other 3 directions, each with probability p_error / 3.\n",
" for a in ACTIONS:\n",
" # main action (intended action)\n",
" main_i, main_j = move_deterministic(i, j, a)\n",
" s_main = pos_to_state[\n",
" (main_i, main_j)\n",
" ] # s_main is the state index of that next cell.\n",
" P[a, s, s_main] += (\n",
" 1 - p_error\n",
" ) # We add probability 1 - p_error to P[a, s, s_main].\n",
"\n",
" # error actions\n",
" other_actions = [\n",
" a2 for a2 in ACTIONS if a2 != a\n",
" ] # other_actions = the 3 actions different from a.\n",
" for a2 in other_actions: # for each of the error action,\n",
" error_i, error_j = move_deterministic(i, j, a2)\n",
" s_error = pos_to_state[(error_i, error_j)] # get its state index s_error\n",
" P[a, s, s_error] += p_error / len(\n",
" other_actions\n",
" ) # add p_error / 3 to P[a, s, s_error]\n",
"# So for each (s,a), probabilities over all s_next sum to 1.\n"
]
},
{
"cell_type": "code",
"execution_count": 549,
"id": "341fe630-8f87-4773-84ad-92d3516e53e2",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Action ↑: [1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n",
" 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n",
" 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]\n",
"Action →: [1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n",
" 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n",
" 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]\n",
"Action ↓: [1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n",
" 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n",
" 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]\n",
"Action ←: [1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n",
" 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n",
" 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]\n"
]
}
],
"source": [
"for a in ACTIONS:\n",
" # For each action a:\n",
" # P[a] is a matrix of shape (n_states, n_states).\n",
" # P[a].sum(axis=1) sums over next states s_next, giving for each state s:\n",
" # We print these row sums.\n",
" # If everything is correct, they should be very close to 1.\n",
"\n",
" probs = P[a].sum(axis=1)\n",
" print(f\"Action {action_names[a]}:\", probs)\n"
]
},
{
"cell_type": "markdown",
"id": "46d23991",
"metadata": {},
"source": [
"## 3. Policy evaluation\n",
"\n",
"### 3.1 Bellman expectation equation"
]
},
{
"cell_type": "code",
"execution_count": 550,
"id": "2fffe0b7",
"metadata": {},
"outputs": [],
"source": [
"def policy_evaluation( # noqa: PLR0913\n",
" policy: np.ndarray,\n",
" P: np.ndarray,\n",
" R: np.ndarray,\n",
" gamma: float,\n",
" theta: float = 1e-6,\n",
" max_iter: int = 10_000,\n",
") -> np.ndarray:\n",
" \"\"\"Evaluate a deterministic policy for the given MDP.\n",
"\n",
" Args:\n",
" policy: array of shape (n_states,), with values in {0,1,2,3}\n",
" P: array of shape (n_actions, n_states, n_states)\n",
" R: array of shape (n_states,)\n",
" gamma: discount factor\n",
" theta: convergence threshold\n",
" max_iter: maximum number of iterations\n",
"\n",
" \"\"\"\n",
" n_states = len(R) # get the number of states\n",
" V = np.zeros(n_states) # initialize the value function\n",
"\n",
" for _it in range(max_iter): # Main iterative loop\n",
" V_new = np.zeros_like(\n",
" V\n",
" ) # Create a new value vector and we will compute an updated value for each state.\n",
"\n",
" # Now we update each state using the Bellman expectation equation\n",
" for s in range(n_states):\n",
" a = policy[s] # Extract the action chosen by the policy in state\n",
" V_new[s] = R[s] + gamma * np.sum(P[a, s, :] * V)\n",
"\n",
" delta = np.max(\n",
" np.abs(V_new - V)\n",
" ) # This measures how much the value function changed in this iteration:\n",
" # If delta is small, the values start to converge; otherwise, we need to keep iterating.\n",
" V = V_new # Update V, i.e. Set the new values for the next iteration.\n",
"\n",
" if delta < theta: # Check convergence: When changes are tiny, we stop.\n",
" break\n",
"\n",
" return V # Return the final value function, this is our estimate for V^{pi}(s), s in the state set.\n"
]
},
{
"cell_type": "code",
"execution_count": 551,
"id": "4c428327",
"metadata": {},
"outputs": [],
"source": [
"def plot_values(V: np.ndarray, title=\"Value function\") -> None:\n",
" \"\"\"Plot the value function V on the maze as a heatmap.\"\"\"\n",
" grid_values = np.full(\n",
" (n_rows, n_cols), np.nan\n",
" ) # Initializes a grid the same size as the maze. Every cell starts as NaN.\n",
" for (\n",
" s,\n",
" (i, j),\n",
" ) in (\n",
" state_to_pos.items()\n",
" ): # recall that state_to_pos maps each state index to its maze coordinates (i,j).\n",
" grid_values[i, j] = V[\n",
" s\n",
" ] # For each reachable cell, we write the value V[s] in the grid.\n",
" # Walls # never get values, and they stay as NaN.\n",
"\n",
" fig, ax = plt.subplots(figsize=figsize)\n",
" im = ax.imshow(grid_values, cmap=\"magma\")\n",
" plt.colorbar(im, ax=ax)\n",
"\n",
" # For each state:\n",
" # Place the text label at (column j, row i).\n",
" # Display value to two decimals.\n",
" # Use white text so it’s visible on the heatmap.\n",
" # Center the text inside each cell.\n",
"\n",
" for s, (i, j) in state_to_pos.items():\n",
" ax.text(\n",
" j, i, f\"{V[s]:.2f}\", ha=\"center\", va=\"center\", color=\"white\", fontsize=9\n",
" )\n",
"\n",
" # Remove axis ticks and set title\n",
" ax.set_xticks([])\n",
" ax.set_yticks([])\n",
" ax.set_title(title)\n",
" plt.show()\n"
]
},
{
"cell_type": "code",
"execution_count": 552,
"id": "c1ab67f0-bd5e-4ffe-b655-aec030401b78",
"metadata": {},
"outputs": [],
"source": [
"def plot_policy(policy: np.ndarray, title=\"Policy\") -> None:\n",
" \"\"\"Plot the given policy on the maze.\"\"\"\n",
" _fig, ax = plt.subplots(figsize=figsize)\n",
" # draw walls as dark cells\n",
" wall_grid = np.zeros((n_rows, n_cols))\n",
" for i in range(n_rows):\n",
" for j in range(n_cols):\n",
" if maze_str[i][j] == \"#\":\n",
" wall_grid[i, j] = 1\n",
" ax.imshow(wall_grid, cmap=\"Greys\", alpha=0.5)\n",
"\n",
" for s, (i, j) in state_to_pos.items():\n",
" cell = maze_str[i][j]\n",
" if cell == \"#\":\n",
" continue\n",
"\n",
" if s in goal_states:\n",
" ax.text(\n",
" j,\n",
" i,\n",
" \"G\",\n",
" ha=\"center\",\n",
" va=\"center\",\n",
" fontsize=14,\n",
" fontweight=\"bold\",\n",
" color=\"blue\",\n",
" )\n",
" elif s in trap_states:\n",
" ax.text(\n",
" j,\n",
" i,\n",
" \"X\",\n",
" ha=\"center\",\n",
" va=\"center\",\n",
" fontsize=14,\n",
" fontweight=\"bold\",\n",
" color=\"red\",\n",
" )\n",
" elif s == start_state:\n",
" ax.text(\n",
" j,\n",
" i,\n",
" \"S\",\n",
" ha=\"center\",\n",
" va=\"center\",\n",
" fontsize=14,\n",
" fontweight=\"bold\",\n",
" color=\"green\",\n",
" )\n",
" else:\n",
" a = policy[s]\n",
" ax.text(\n",
" j,\n",
" i,\n",
" action_names[a],\n",
" ha=\"center\",\n",
" va=\"center\",\n",
" fontsize=14,\n",
" color=\"black\",\n",
" )\n",
"\n",
" ax.set_xticks(np.arange(-0.5, n_cols, 1))\n",
" ax.set_yticks(np.arange(-0.5, n_rows, 1))\n",
" ax.set_xticklabels([])\n",
" ax.set_yticklabels([])\n",
" ax.grid(True)\n",
" ax.set_title(title)\n",
" plt.show()\n"
]
},
{
"cell_type": "markdown",
"id": "813121a9",
"metadata": {},
"source": [
"### 3.3 Evaluating a random policy"
]
},
{
"cell_type": "code",
"execution_count": 553,
"id": "ceb5dfe2",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[0 3 2 1 1 3 0 2 0 0 2 3 2 3 2 3 2 0 3 1 2 1 0 3 3 2 1 3 2 1 1 0 0 2 3 0 3\n",
" 3 1 2 0 3 2 1 0 3 1 3 2 3 3 0 1 1 1 0 2 0 2 2 3 2]\n"
]
}
],
"source": [
"# Random policy: for each state, pick a random action\n",
"random_policy = rng.integers(low=0, high=len(ACTIONS), size=n_states)\n",
"\n",
"print(random_policy)"
]
},
{
"cell_type": "code",
"execution_count": 554,
"id": "8f3e2ac2",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Value function under random policy:\n",
"[ -0.2 -0.295 -0.534 -1.301 -1.394 -1.467 -0.827 -1.176 -20.\n",
" -0.2 -0.207 -6.086 -0.548 -0.2 -0.201 -0.204 -0.28 -0.481\n",
" -20. -0.546 -0.566 -0.2 -1.126 -0.588 -0.201 -0.203 -0.209\n",
" -20. -20. -1.769 -1.186 -1.222 -0.229 -20. -1.944 -0.862\n",
" -0.824 -1.381 -18.279 -20. -7.557 -6.924 -0.44 -5.78 -17.248\n",
" -7.364 -0.214 -0.207 -18.427 -17.386 -16.41 -16.347 -17.519 -18.483\n",
" -20. -0.013 -20. -15.666 -20. -20. 20. 5.496]\n"
]
}
],
"source": [
"V_random = policy_evaluation(policy=random_policy, P=P, R=R, gamma=gamma)\n",
"print(\"Value function under random policy:\")\n",
"print(V_random)\n"
]
},
{
"cell_type": "code",
"execution_count": 555,
"id": "cf45291e",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 800x800 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot_policy(policy=random_policy, title=\"Policy\")\n"
]
},
{
"cell_type": "code",
"execution_count": 557,
"id": "5a82a3b7",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 800x800 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 800x800 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"my_policy = [\n",
" A_DOWN,\n",
" A_DOWN,\n",
" A_LEFT,\n",
" A_LEFT,\n",
" A_LEFT,\n",
" A_LEFT,\n",
" A_LEFT,\n",
" A_LEFT,\n",
" A_LEFT,\n",
" A_DOWN,\n",
" A_DOWN,\n",
" A_UP,\n",
" A_UP,\n",
" A_DOWN,\n",
" A_LEFT,\n",
" A_LEFT,\n",
" A_LEFT,\n",
" A_LEFT,\n",
" A_UP,\n",
" A_UP,\n",
" A_LEFT,\n",
" A_DOWN,\n",
" A_UP,\n",
" A_UP,\n",
" A_RIGHT,\n",
" A_RIGHT,\n",
" A_DOWN,\n",
" A_UP,\n",
" A_RIGHT,\n",
" A_RIGHT,\n",
" A_RIGHT,\n",
" A_UP,\n",
" A_DOWN,\n",
" A_UP,\n",
" A_RIGHT,\n",
" A_RIGHT,\n",
" A_RIGHT,\n",
" A_RIGHT,\n",
" A_DOWN,\n",
" A_RIGHT,\n",
" A_RIGHT,\n",
" A_RIGHT,\n",
" A_DOWN,\n",
" A_UP,\n",
" A_DOWN,\n",
" A_UP,\n",
" A_RIGHT,\n",
" A_DOWN,\n",
" A_UP,\n",
" A_LEFT,\n",
" A_LEFT,\n",
" A_RIGHT,\n",
" A_RIGHT,\n",
" A_UP,\n",
" A_LEFT,\n",
" A_DOWN,\n",
" A_UP,\n",
" A_UP,\n",
" A_LEFT,\n",
" A_UP,\n",
" A_DOWN,\n",
" A_LEFT,\n",
"]\n",
"\n",
"V_my_policy = policy_evaluation(policy=my_policy, P=P, R=R, gamma=gamma)\n",
"\n",
"plot_values(V=V_my_policy, title=\"Value function: my policy\")\n",
"plot_policy(policy=my_policy, title=\"My policy\")\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "446c93e4",
"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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