mirror of
https://github.com/ArthurDanjou/ArtStudies.git
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Arthur DANJOU
211259cd2a
- Updated the Q-Learning model checkpoint (q_learning.pkl) to reflect recent training improvements. - Revised the training curves plot (Q-Learning_training_curves.png) to visualize the latest performance metrics.
1737 lines
250 KiB
Plaintext
1737 lines
250 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "fef45687",
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"metadata": {},
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"source": [
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"# RL Project: Atari Tennis Tournament\n",
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"\n",
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"This notebook implements four Reinforcement Learning algorithms to play Atari Tennis (`ALE/Tennis-v5` via Gymnasium):\n",
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"\n",
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"1. **SARSA** — Semi-gradient SARSA with linear approximation (inspired by Lab 7, on-policy update from Lab 5B)\n",
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"2. **Q-Learning** — Off-policy linear approximation (inspired by Lab 5B)\n",
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"\n",
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"Each agent is **pre-trained independently** against the built-in Atari AI opponent, then evaluated in a comparative tournament."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 51,
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"id": "b50d7174",
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"metadata": {},
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"outputs": [],
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"source": [
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"import pickle\n",
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"from collections import deque\n",
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"from pathlib import Path\n",
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"\n",
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"import ale_py # noqa: F401 — registers ALE environments\n",
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"from pettingzoo.atari import tennis_v3\n",
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"from tqdm.auto import tqdm\n",
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"\n",
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"import matplotlib.pyplot as plt\n",
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"import numpy as np\n",
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"\n",
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"import torch\n",
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"from torch import nn, optim\n"
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]
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},
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{
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"cell_type": "markdown",
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"id": "86047166",
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"metadata": {},
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"source": [
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"# Configuration & Checkpoints\n",
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"\n",
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"We use a **checkpoint** system (`pickle` serialization) to save and restore trained agent weights. This enables an incremental workflow:\n",
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"- Train one agent at a time and save its weights\n",
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"- Resume later without retraining previous agents\n",
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"- Load all checkpoints for the final evaluation"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 52,
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"id": "ff3486a4",
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"metadata": {},
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"outputs": [],
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"source": [
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"CHECKPOINT_DIR = Path(\"checkpoints\")\n",
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"CHECKPOINT_DIR.mkdir(parents=True, exist_ok=True)\n",
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"\n",
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"\n",
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"def get_path(name: str) -> Path:\n",
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" \"\"\"Return the checkpoint path for an agent (.pkl).\"\"\"\n",
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" base = name.lower().replace(\" \", \"_\").replace(\"-\", \"_\")\n",
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" return CHECKPOINT_DIR / (base + \".pkl\")\n"
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]
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},
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{
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"cell_type": "markdown",
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"id": "ec691487",
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"metadata": {},
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"source": [
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"# Utility Functions\n",
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"\n",
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"## Observation Normalization\n",
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"\n",
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"The Tennis environment produces image observations of shape `(4, 84, 84)` after preprocessing (grayscale + resize + frame stack).\n",
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"We normalize them into 1D `float64` vectors divided by 255, as in Lab 7 (continuous feature normalization).\n",
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"\n",
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"## ε-greedy Policy\n",
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"\n",
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"Follows the pattern from Lab 5B (`epsilon_greedy`) and Lab 7 (`epsilon_greedy_action`):\n",
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"- With probability ε: random action (exploration)\n",
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"- With probability 1−ε: action maximizing $\\hat{q}(s, a)$ with uniform tie-breaking (`np.flatnonzero`)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 53,
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"id": "be85c130",
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"metadata": {},
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"outputs": [],
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"source": [
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"def normalize_obs(observation: np.ndarray) -> np.ndarray:\n",
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" \"\"\"Flatten and normalize an observation to a 1D float64 vector.\n",
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"\n",
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" Args:\n",
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" observation: Raw observation array from the environment.\n",
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"\n",
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" Returns:\n",
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" 1D numpy array of dtype float64, values in [0, 1].\n",
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"\n",
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" \"\"\"\n",
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" return observation.flatten().astype(np.float64) / 255.0\n",
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"\n",
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"\n",
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"def epsilon_greedy(\n",
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" q_values: np.ndarray,\n",
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" epsilon: float,\n",
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" rng: np.random.Generator,\n",
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") -> int:\n",
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" \"\"\"Select an action using an ε-greedy policy with fair tie-breaking.\n",
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"\n",
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" Follows the same logic as Lab 5B epsilon_greedy and Lab 7 epsilon_greedy_action:\n",
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" - With probability epsilon: choose a random action (exploration).\n",
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" - With probability 1-epsilon: choose the action with highest Q-value (exploitation).\n",
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" - If multiple actions share the maximum Q-value, break ties uniformly at random.\n",
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"\n",
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" Handles edge cases: empty q_values, NaN/Inf values.\n",
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"\n",
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" Args:\n",
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" q_values: Array of Q-values for each action, shape (n_actions,).\n",
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" epsilon: Exploration probability in [0, 1].\n",
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" rng: NumPy random number generator.\n",
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"\n",
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" Returns:\n",
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" Selected action index.\n",
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"\n",
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" \"\"\"\n",
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" q_values = np.asarray(q_values, dtype=np.float64).reshape(-1)\n",
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"\n",
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" if q_values.size == 0:\n",
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" msg = \"q_values is empty.\"\n",
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" raise ValueError(msg)\n",
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"\n",
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" if rng.random() < epsilon:\n",
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" return int(rng.integers(0, q_values.size))\n",
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"\n",
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" finite_mask = np.isfinite(q_values)\n",
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" if not np.any(finite_mask):\n",
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" return int(rng.integers(0, q_values.size))\n",
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"\n",
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" safe_q = q_values.copy()\n",
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" safe_q[~finite_mask] = -np.inf\n",
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" max_val = np.max(safe_q)\n",
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" best = np.flatnonzero(safe_q == max_val)\n",
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"\n",
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" if best.size == 0:\n",
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" return int(rng.integers(0, q_values.size))\n",
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"\n",
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" return int(rng.choice(best))\n"
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]
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},
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{
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"cell_type": "markdown",
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"id": "bb53da28",
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"metadata": {},
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"source": [
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"# Agent Definitions\n",
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"\n",
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"## Base Class `Agent`\n",
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"\n",
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"Common interface for all agents, same signatures: `get_action`, `update`, `save`, `load`.\n",
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"Serialization uses `pickle` (compatible with numpy arrays)."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 54,
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"id": "ded9b1fb",
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"metadata": {},
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"outputs": [],
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"source": [
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"class Agent:\n",
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" \"\"\"Base class for reinforcement learning agents.\n",
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"\n",
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" All agents share this interface so they are compatible with the tournament system.\n",
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" \"\"\"\n",
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"\n",
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" def __init__(self, seed: int, action_space: int) -> None:\n",
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" \"\"\"Initialize the agent with its action space and a reproducible RNG.\"\"\"\n",
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" self.action_space = action_space\n",
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" self.rng = np.random.default_rng(seed=seed)\n",
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"\n",
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" def get_action(self, observation: np.ndarray, epsilon: float = 0.0) -> int:\n",
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" \"\"\"Select an action from the current observation.\"\"\"\n",
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" raise NotImplementedError\n",
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"\n",
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" def update(\n",
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" self,\n",
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" state: np.ndarray,\n",
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" action: int,\n",
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" reward: float,\n",
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" next_state: np.ndarray,\n",
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" done: bool,\n",
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" next_action: int | None = None,\n",
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" agent_id: str = \"single\",\n",
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" ) -> None:\n",
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" \"\"\"Update the agent's internal state based on a transition.\"\"\"\n",
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"\n",
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" def save(self, filename: str) -> None:\n",
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" \"\"\"Save the agent state to disk using pickle.\"\"\"\n",
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" with Path(filename).open(\"wb\") as f:\n",
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" pickle.dump(self.__dict__, f)\n",
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"\n",
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" def load(self, filename: str) -> None:\n",
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" \"\"\"Load the agent state from disk.\"\"\"\n",
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" with Path(filename).open(\"rb\") as f:\n",
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" path = Path(filename).resolve()\n",
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" ckpt_root = CHECKPOINT_DIR.resolve()\n",
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" if ckpt_root not in path.parents:\n",
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" msg = f\"Refusing to load checkpoint outside '{ckpt_root}': {path}\"\n",
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" raise ValueError(msg)\n",
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" if path.suffix != \".pkl\":\n",
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" msg = f\"Unsupported checkpoint format: {path.suffix}\"\n",
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" raise ValueError(msg)\n",
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"\n",
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" state = pickle.load(f) # noqa: S301 - trusted local checkpoints only\n",
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" if not isinstance(state, dict):\n",
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" msg = \"Invalid checkpoint payload: expected a dict.\"\n",
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" raise TypeError(msg)\n",
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"\n",
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" self.__dict__.update(state)\n"
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]
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},
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{
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"cell_type": "markdown",
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"id": "8a4eae79",
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"metadata": {},
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"source": [
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"## Random Agent (baseline)\n",
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"\n",
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"Serves as a reference to evaluate the performance of learning agents."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 55,
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"id": "78bdc9d2",
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"metadata": {},
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"outputs": [],
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"source": [
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"class RandomAgent(Agent):\n",
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" \"\"\"A simple agent that selects actions uniformly at random (baseline).\"\"\"\n",
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"\n",
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" def get_action(self, observation: np.ndarray, epsilon: float = 0.0) -> int:\n",
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" \"\"\"Select a random action, ignoring the observation and epsilon.\"\"\"\n",
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" _ = observation, epsilon\n",
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" return int(self.rng.integers(0, self.action_space))\n"
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]
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},
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{
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"cell_type": "markdown",
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"id": "5f679032",
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"metadata": {},
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"source": [
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"## SARSA Agent — Linear Approximation (Semi-gradient)\n",
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"\n",
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"This agent combines:\n",
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"- **Linear approximation** from Lab 7 (`SarsaAgent`): $\\hat{q}(s, a; \\mathbf{W}) = \\mathbf{W}_a^\\top \\phi(s)$\n",
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"- **On-policy SARSA update** from Lab 5B (`train_sarsa`): $\\delta = r + \\gamma \\hat{q}(s', a') - \\hat{q}(s, a)$\n",
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"\n",
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"The semi-gradient update rule is:\n",
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"$$W_a \\leftarrow W_a + \\alpha \\cdot \\delta \\cdot \\phi(s)$$\n",
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"\n",
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"where $\\phi(s)$ is the normalized observation vector (analogous to tile coding features in Lab 7, but in dense form)."
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]
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},
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{
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||
"cell_type": "code",
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"execution_count": 56,
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"id": "c124ed9a",
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"metadata": {},
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||
"outputs": [],
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||
"source": [
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"class SarsaAgent(Agent):\n",
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" \"\"\"Semi-gradient SARSA agent with linear function approximation.\n",
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"\n",
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" Inspired by:\n",
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" - Lab 7 SarsaAgent: linear q(s,a) = W_a . phi(s), semi-gradient update\n",
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" - Lab 5B train_sarsa: on-policy TD target using Q(s', a')\n",
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"\n",
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" The weight matrix W has shape (n_actions, n_features).\n",
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" For a given state s, q(s, a) = W[a] @ phi(s) is the dot product\n",
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" of the action's weight row with the normalized observation.\n",
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" \"\"\"\n",
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"\n",
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" def __init__(\n",
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" self,\n",
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" n_features: int,\n",
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" n_actions: int,\n",
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" alpha: float = 0.001,\n",
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" gamma: float = 0.99,\n",
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" seed: int = 42,\n",
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" ) -> None:\n",
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" \"\"\"Initialize SARSA agent with linear weights.\n",
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"\n",
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" Args:\n",
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" n_features: Dimension of the feature vector phi(s).\n",
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" n_actions: Number of discrete actions.\n",
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" alpha: Learning rate (kept small for high-dim features).\n",
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" gamma: Discount factor.\n",
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" seed: RNG seed for reproducibility.\n",
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"\n",
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" \"\"\"\n",
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" super().__init__(seed, n_actions)\n",
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" self.n_features = n_features\n",
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" self.alpha = alpha\n",
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" self.gamma = gamma\n",
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" self.W = np.zeros((n_actions, n_features), dtype=np.float64)\n",
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"\n",
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" def _q_values(self, phi: np.ndarray) -> np.ndarray:\n",
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" \"\"\"Compute Q-values for all actions given feature vector phi(s).\n",
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"\n",
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" Equivalent to Lab 7's self.q(s, a) = self.w[idx].sum()\n",
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" but using dense linear approximation: q(s, a) = W[a] @ phi.\n",
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"\n",
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" Args:\n",
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" phi: Normalized feature vector, shape (n_features,).\n",
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"\n",
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" Returns:\n",
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" Array of Q-values, shape (n_actions,).\n",
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"\n",
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" \"\"\"\n",
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" return self.W @ phi\n",
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"\n",
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" def get_action(self, observation: np.ndarray, epsilon: float = 0.0) -> int:\n",
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" \"\"\"Select action using ε-greedy policy over linear Q-values.\n",
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"\n",
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" Same pattern as Lab 7 SarsaAgent.eps_greedy:\n",
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" compute q-values for all actions, then apply epsilon_greedy.\n",
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" \"\"\"\n",
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" phi = normalize_obs(observation)\n",
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" q_vals = self._q_values(phi)\n",
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" return epsilon_greedy(q_vals, epsilon, self.rng)\n",
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"\n",
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" def update(\n",
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" self,\n",
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" state: np.ndarray,\n",
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" action: int,\n",
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" reward: float,\n",
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" next_state: np.ndarray,\n",
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" done: bool,\n",
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" next_action: int | None = None,\n",
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" agent_id: str = \"single\",\n",
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" ) -> None:\n",
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" \"\"\"Perform one semi-gradient SARSA update.\n",
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"\n",
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" Follows the SARSA update from Lab 5B train_sarsa:\n",
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" td_target = r + gamma * Q(s', a') * (0 if done else 1)\n",
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" Q(s, a) += alpha * (td_target - Q(s, a))\n",
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"\n",
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" In continuous form with linear approximation (Lab 7 SarsaAgent.update):\n",
|
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" delta = target - q(s, a)\n",
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" W[a] += alpha * delta * phi(s)\n",
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" \"\"\"\n",
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" phi = np.nan_to_num(normalize_obs(state), nan=0.0, posinf=0.0, neginf=0.0)\n",
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" q_sa = float(self.W[action] @ phi)\n",
|
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" if not np.isfinite(q_sa):\n",
|
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" q_sa = 0.0\n",
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"\n",
|
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" if done:\n",
|
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" target = reward\n",
|
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" else:\n",
|
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" phi_next = np.nan_to_num(\n",
|
||
" normalize_obs(next_state), nan=0.0, posinf=0.0, neginf=0.0,\n",
|
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" )\n",
|
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" if next_action is None:\n",
|
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" next_action = 0\n",
|
||
" q_sp_ap = float(self.W[next_action] @ phi_next)\n",
|
||
" if not np.isfinite(q_sp_ap):\n",
|
||
" q_sp_ap = 0.0\n",
|
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" target = float(reward) + self.gamma * q_sp_ap\n",
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"\n",
|
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" if not np.isfinite(target):\n",
|
||
" return\n",
|
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"\n",
|
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" delta = float(target - q_sa)\n",
|
||
" if not np.isfinite(delta):\n",
|
||
" return\n",
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"\n",
|
||
" td_step = float(np.clip(delta, -1_000.0, 1_000.0))\n",
|
||
" self.W[action] += self.alpha * td_step * phi\n",
|
||
" self.W[action] = np.nan_to_num(self.W[action], nan=0.0, posinf=1e6, neginf=-1e6)\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "d4e18536",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Q-Learning Agent — Linear Approximation (Off-policy)\n",
|
||
"\n",
|
||
"Same architecture as SARSA but with the **off-policy update** from Lab 5B (`train_q_learning`):\n",
|
||
"\n",
|
||
"$$\\delta = r + \\gamma \\max_{a'} \\hat{q}(s', a') - \\hat{q}(s, a)$$\n",
|
||
"\n",
|
||
"The key difference from SARSA: we use $\\max_{a'} Q(s', a')$ instead of $Q(s', a')$ where $a'$ is the action actually chosen. This allows learning the optimal policy independently of the exploration policy."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 57,
|
||
"id": "f5b5b9ea",
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"class QLearningAgent(Agent):\n",
|
||
" \"\"\"Q-Learning agent with linear function approximation (off-policy).\n",
|
||
"\n",
|
||
" Inspired by:\n",
|
||
" - Lab 5B train_q_learning: off-policy TD target using max_a' Q(s', a')\n",
|
||
" - Lab 7 SarsaAgent: linear approximation q(s,a) = W[a] @ phi(s)\n",
|
||
"\n",
|
||
" The only difference from SarsaAgent is the TD target:\n",
|
||
" SARSA uses Q(s', a') (on-policy), Q-Learning uses max_a' Q(s', a') (off-policy).\n",
|
||
" \"\"\"\n",
|
||
"\n",
|
||
" def __init__(\n",
|
||
" self,\n",
|
||
" n_features: int,\n",
|
||
" n_actions: int,\n",
|
||
" alpha: float = 0.001,\n",
|
||
" gamma: float = 0.99,\n",
|
||
" seed: int = 42,\n",
|
||
" ) -> None:\n",
|
||
" \"\"\"Initialize Q-Learning agent with linear weights.\n",
|
||
"\n",
|
||
" Args:\n",
|
||
" n_features: Dimension of the feature vector phi(s).\n",
|
||
" n_actions: Number of discrete actions.\n",
|
||
" alpha: Learning rate.\n",
|
||
" gamma: Discount factor.\n",
|
||
" seed: RNG seed.\n",
|
||
"\n",
|
||
" \"\"\"\n",
|
||
" super().__init__(seed, n_actions)\n",
|
||
" self.n_features = n_features\n",
|
||
" self.alpha = alpha\n",
|
||
" self.gamma = gamma\n",
|
||
" self.W = np.zeros((n_actions, n_features), dtype=np.float64)\n",
|
||
"\n",
|
||
" def _q_values(self, phi: np.ndarray) -> np.ndarray:\n",
|
||
" \"\"\"Compute Q-values for all actions: q(s, a) = W[a] @ phi for each a.\"\"\"\n",
|
||
" return self.W @ phi\n",
|
||
"\n",
|
||
" def get_action(self, observation: np.ndarray, epsilon: float = 0.0) -> int:\n",
|
||
" \"\"\"Select action using ε-greedy policy over linear Q-values.\"\"\"\n",
|
||
" phi = normalize_obs(observation)\n",
|
||
" q_vals = self._q_values(phi)\n",
|
||
" return epsilon_greedy(q_vals, epsilon, self.rng)\n",
|
||
"\n",
|
||
" def update(\n",
|
||
" self,\n",
|
||
" state: np.ndarray,\n",
|
||
" action: int,\n",
|
||
" reward: float,\n",
|
||
" next_state: np.ndarray,\n",
|
||
" done: bool,\n",
|
||
" next_action: int | None = None,\n",
|
||
" agent_id: str = \"single\",\n",
|
||
" ) -> None:\n",
|
||
" \"\"\"Perform one Q-learning update.\n",
|
||
"\n",
|
||
" Follows Lab 5B train_q_learning:\n",
|
||
" td_target = r + gamma * max(Q[s2]) * (0 if terminated else 1)\n",
|
||
" Q[s, a] += alpha * (td_target - Q[s, a])\n",
|
||
"\n",
|
||
" In continuous form with linear approximation:\n",
|
||
" delta = target - q(s, a)\n",
|
||
" W[a] += alpha * delta * phi(s)\n",
|
||
" \"\"\"\n",
|
||
" _ = next_action\n",
|
||
" phi = np.nan_to_num(normalize_obs(state), nan=0.0, posinf=0.0, neginf=0.0)\n",
|
||
" q_sa = float(self.W[action] @ phi)\n",
|
||
" if not np.isfinite(q_sa):\n",
|
||
" q_sa = 0.0\n",
|
||
"\n",
|
||
" if done:\n",
|
||
" target = reward\n",
|
||
" else:\n",
|
||
" phi_next = np.nan_to_num(\n",
|
||
" normalize_obs(next_state), nan=0.0, posinf=0.0, neginf=0.0,\n",
|
||
" )\n",
|
||
" q_next_all = self._q_values(phi_next)\n",
|
||
" q_next_max = float(np.max(q_next_all))\n",
|
||
" if not np.isfinite(q_next_max):\n",
|
||
" q_next_max = 0.0\n",
|
||
" target = float(reward) + self.gamma * q_next_max\n",
|
||
"\n",
|
||
" if not np.isfinite(target):\n",
|
||
" return\n",
|
||
"\n",
|
||
" delta = float(target - q_sa)\n",
|
||
" if not np.isfinite(delta):\n",
|
||
" return\n",
|
||
"\n",
|
||
" td_step = float(np.clip(delta, -1_000.0, 1_000.0))\n",
|
||
" self.W[action] += self.alpha * td_step * phi\n",
|
||
" self.W[action] = np.nan_to_num(self.W[action], nan=0.0, posinf=1e6, neginf=-1e6)\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "79e6b39f",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Monte Carlo Agent — Linear Approximation (First-visit)\n",
|
||
"\n",
|
||
"This agent is inspired by Lab 4 (`mc_control_epsilon_soft`):\n",
|
||
"- Accumulates transitions in an episode buffer `(state, action, reward)`\n",
|
||
"- At the end of the episode (`done=True`), computes **cumulative returns** by traversing the buffer backward:\n",
|
||
" $$G \\leftarrow \\gamma \\cdot G + r$$\n",
|
||
"- Updates weights with the semi-gradient rule:\n",
|
||
" $$W_a \\leftarrow W_a + \\alpha \\cdot (G - \\hat{q}(s, a)) \\cdot \\phi(s)$$\n",
|
||
"\n",
|
||
"Unlike TD methods (SARSA, Q-Learning), Monte Carlo waits for the complete episode to finish before updating.\n",
|
||
"\n",
|
||
"> **Note**: This agent currently has **checkpoint loading issues** — the saved weights fail to restore properly, causing the agent to behave as if untrained during evaluation. The training code itself works correctly."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 58,
|
||
"id": "7a3aa454",
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"class MonteCarloAgent(Agent):\n",
|
||
" \"\"\"Monte Carlo control agent with linear function approximation.\"\"\"\n",
|
||
"\n",
|
||
" def __init__(\n",
|
||
" self,\n",
|
||
" n_features: int,\n",
|
||
" n_actions: int,\n",
|
||
" alpha: float = 0.001,\n",
|
||
" gamma: float = 0.99,\n",
|
||
" seed: int = 42,\n",
|
||
" ) -> None:\n",
|
||
" \"\"\"Initialize Monte Carlo agent with linear weights and episode buffers.\"\"\"\n",
|
||
" super().__init__(seed, n_actions)\n",
|
||
" self.n_features = n_features\n",
|
||
" self.alpha = alpha\n",
|
||
" self.gamma = gamma\n",
|
||
" self.W = np.zeros((n_actions, n_features), dtype=np.float32)\n",
|
||
" self._obs_buf: dict[str, list[np.ndarray]] = {}\n",
|
||
" self._act_buf: dict[str, list[int]] = {}\n",
|
||
" self._rew_buf: dict[str, list[float]] = {}\n",
|
||
"\n",
|
||
" def _q_values(self, phi: np.ndarray) -> np.ndarray:\n",
|
||
" \"\"\"Compute Q-values.\"\"\"\n",
|
||
" return self.W @ phi\n",
|
||
"\n",
|
||
" def get_action(self, observation: np.ndarray, epsilon: float = 0.0) -> int:\n",
|
||
" \"\"\"Select action using epsilon-greedy policy over linear Q-values.\"\"\"\n",
|
||
" phi = observation.flatten().astype(np.float32) / np.float32(255.0)\n",
|
||
" q_vals = self._q_values(phi)\n",
|
||
" return epsilon_greedy(q_vals, epsilon, self.rng)\n",
|
||
"\n",
|
||
" def update(\n",
|
||
" self,\n",
|
||
" state: np.ndarray,\n",
|
||
" action: int,\n",
|
||
" reward: float,\n",
|
||
" next_state: np.ndarray,\n",
|
||
" done: bool,\n",
|
||
" next_action: int | None = None,\n",
|
||
" agent_id: str = \"single\",\n",
|
||
" ) -> None:\n",
|
||
" \"\"\"Accumulate episode transitions and update weights at episode end.\"\"\"\n",
|
||
" _ = next_state, next_action\n",
|
||
"\n",
|
||
" if agent_id not in self._obs_buf:\n",
|
||
" self._obs_buf[agent_id] = []\n",
|
||
" self._act_buf[agent_id] = []\n",
|
||
" self._rew_buf[agent_id] = []\n",
|
||
"\n",
|
||
" self._obs_buf[agent_id].append(state)\n",
|
||
" self._act_buf[agent_id].append(action)\n",
|
||
" self._rew_buf[agent_id].append(reward)\n",
|
||
"\n",
|
||
" if not done:\n",
|
||
" return\n",
|
||
"\n",
|
||
" n = len(self._rew_buf[agent_id])\n",
|
||
" actions = np.array(self._act_buf[agent_id], dtype=np.intp)\n",
|
||
"\n",
|
||
" returns = np.empty(n, dtype=np.float32)\n",
|
||
" G = np.float32(0.0)\n",
|
||
" gamma32 = np.float32(self.gamma)\n",
|
||
" for i in range(n - 1, -1, -1):\n",
|
||
" G = gamma32 * G + np.float32(self._rew_buf[agent_id][i])\n",
|
||
" returns[i] = G\n",
|
||
"\n",
|
||
" alpha32 = np.float32(self.alpha)\n",
|
||
" chunk_size = 500\n",
|
||
" for start in range(0, n, chunk_size):\n",
|
||
" end = min(start + chunk_size, n)\n",
|
||
" cs = end - start\n",
|
||
"\n",
|
||
" raw = np.array(self._obs_buf[agent_id][start:end])\n",
|
||
" phi = raw.reshape(cs, -1).astype(np.float32)\n",
|
||
" phi /= np.float32(255.0)\n",
|
||
"\n",
|
||
" ca = actions[start:end]\n",
|
||
" q_sa = np.einsum(\"ij,ij->i\", self.W[ca], phi)\n",
|
||
"\n",
|
||
" deltas = np.clip(returns[start:end] - q_sa, -1000.0, 1000.0)\n",
|
||
"\n",
|
||
" for a in range(self.action_space):\n",
|
||
" mask = ca == a\n",
|
||
" if not np.any(mask):\n",
|
||
" continue\n",
|
||
" self.W[a] += alpha32 * (deltas[mask] @ phi[mask])\n",
|
||
"\n",
|
||
" self.W = np.nan_to_num(self.W, nan=0.0, posinf=1e6, neginf=-1e6)\n",
|
||
"\n",
|
||
" self._obs_buf[agent_id].clear()\n",
|
||
" self._act_buf[agent_id].clear()\n",
|
||
" self._rew_buf[agent_id].clear()\n",
|
||
"\n",
|
||
" def save(self, filename: str) -> None:\n",
|
||
" \"\"\"Save agent state, clearing episode buffers first to avoid stale data.\"\"\"\n",
|
||
" self._obs_buf.clear()\n",
|
||
" self._act_buf.clear()\n",
|
||
" self._rew_buf.clear()\n",
|
||
" super().save(filename)\n",
|
||
"\n",
|
||
" def load(self, filename: str) -> None:\n",
|
||
" \"\"\"Load agent state and ensure correct dtype for weights.\"\"\"\n",
|
||
" super().load(filename)\n",
|
||
" self.W = np.asarray(self.W, dtype=np.float32)\n",
|
||
" self._obs_buf = {}\n",
|
||
" self._act_buf = {}\n",
|
||
" self._rew_buf = {}\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "d5766fe9",
|
||
"metadata": {},
|
||
"source": [
|
||
"## DQN Agent — PyTorch MLP with Experience Replay and Target Network\n",
|
||
"\n",
|
||
"This agent implements the Deep Q-Network (DQN) using **PyTorch** for GPU-accelerated training (MPS on Apple Silicon).\n",
|
||
"\n",
|
||
"**Network architecture** (same structure as before, now as `torch.nn.Module`):\n",
|
||
"$$\\text{Input}(n\\_features) \\to \\text{Linear}(256) \\to \\text{ReLU} \\to \\text{Linear}(256) \\to \\text{ReLU} \\to \\text{Linear}(n\\_actions)$$\n",
|
||
"\n",
|
||
"**Key techniques** (inspired by Lab 6A Dyna-Q + classic DQN):\n",
|
||
"- **Experience Replay**: circular buffer of transitions, sampled as minibatches for off-policy updates\n",
|
||
"- **Target Network**: periodically synchronized copy of the Q-network, stabilizes learning\n",
|
||
"- **Gradient clipping**: prevents exploding gradients in deep networks\n",
|
||
"- **GPU acceleration**: tensors on MPS/CUDA device for fast forward/backward passes\n",
|
||
"\n",
|
||
"> **Note**: This agent currently has **checkpoint loading issues** — the saved `.pt` checkpoint fails to restore properly (device mismatch / state dict incompatibility), causing errors during evaluation. The training code itself works correctly."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 59,
|
||
"id": "9c777493",
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"class QNetwork(nn.Module):\n",
|
||
" \"\"\"MLP Q-network: Input -> 256 -> ReLU -> 256 -> ReLU -> n_actions.\"\"\"\n",
|
||
"\n",
|
||
" def __init__(self, n_features: int, n_actions: int) -> None:\n",
|
||
" \"\"\"Initialize the Q-network architecture.\"\"\"\n",
|
||
" super().__init__()\n",
|
||
" self.net = nn.Sequential(\n",
|
||
" nn.Linear(n_features, 256),\n",
|
||
" nn.ReLU(),\n",
|
||
" nn.Linear(256, 256),\n",
|
||
" nn.ReLU(),\n",
|
||
" nn.Linear(256, n_actions),\n",
|
||
" )\n",
|
||
"\n",
|
||
" def forward(self, x: torch.Tensor) -> torch.Tensor:\n",
|
||
" \"\"\"Compute Q-values for input state tensor x.\"\"\"\n",
|
||
" return self.net(x)\n",
|
||
"\n",
|
||
"\n",
|
||
"class ReplayBuffer:\n",
|
||
" \"\"\"Fixed-size circular replay buffer storing (s, a, r, s', done) transitions.\"\"\"\n",
|
||
"\n",
|
||
" def __init__(self, capacity: int) -> None:\n",
|
||
" \"\"\"Initialize the replay buffer with a maximum capacity.\"\"\"\n",
|
||
" self.buffer: deque[tuple[np.ndarray, int, float, np.ndarray, bool]] = deque(maxlen=capacity)\n",
|
||
"\n",
|
||
" def push(self, state: np.ndarray, action: int, reward: float, next_state: np.ndarray, done: bool) -> None:\n",
|
||
" \"\"\"Add a transition to the replay buffer.\"\"\"\n",
|
||
" self.buffer.append((state, action, reward, next_state, done))\n",
|
||
"\n",
|
||
" def sample(self, batch_size: int, rng: np.random.Generator) -> tuple[np.ndarray, ...]:\n",
|
||
" \"\"\"Sample a random minibatch of transitions from the buffer.\"\"\"\n",
|
||
" indices = rng.choice(len(self.buffer), size=batch_size, replace=False)\n",
|
||
" batch = [self.buffer[i] for i in indices]\n",
|
||
" states = np.array([t[0] for t in batch])\n",
|
||
" actions = np.array([t[1] for t in batch])\n",
|
||
" rewards = np.array([t[2] for t in batch])\n",
|
||
" next_states = np.array([t[3] for t in batch])\n",
|
||
" dones = np.array([t[4] for t in batch], dtype=np.float32)\n",
|
||
" return states, actions, rewards, next_states, dones\n",
|
||
"\n",
|
||
" def __len__(self) -> int:\n",
|
||
" \"\"\"Return the current number of transitions stored in the buffer.\"\"\"\n",
|
||
" return len(self.buffer)\n",
|
||
"\n",
|
||
"\n",
|
||
"class DQNAgent(Agent):\n",
|
||
" \"\"\"Deep Q-Network agent using PyTorch with GPU acceleration (MPS/CUDA).\n",
|
||
"\n",
|
||
" Inspired by:\n",
|
||
" - Lab 6A Dyna-Q: experience replay (store transitions, sample for updates)\n",
|
||
" - Classic DQN (Mnih et al., 2015): target network, minibatch SGD\n",
|
||
"\n",
|
||
" Uses Adam optimizer and Huber loss (smooth L1) for stable training.\n",
|
||
" \"\"\"\n",
|
||
"\n",
|
||
" def __init__(\n",
|
||
" self,\n",
|
||
" n_features: int,\n",
|
||
" n_actions: int,\n",
|
||
" lr: float = 1e-4,\n",
|
||
" gamma: float = 0.99,\n",
|
||
" buffer_size: int = 50_000,\n",
|
||
" batch_size: int = 64,\n",
|
||
" target_update_freq: int = 1000,\n",
|
||
" train_freq: int = 4,\n",
|
||
" seed: int = 42,\n",
|
||
" ) -> None:\n",
|
||
" \"\"\"Initialize DQN agent.\n",
|
||
"\n",
|
||
" Args:\n",
|
||
" n_features: Input feature dimension.\n",
|
||
" n_actions: Number of discrete actions.\n",
|
||
" lr: Learning rate for Adam optimizer.\n",
|
||
" gamma: Discount factor.\n",
|
||
" buffer_size: Maximum replay buffer capacity.\n",
|
||
" batch_size: Minibatch size for updates.\n",
|
||
" target_update_freq: Steps between target network syncs.\n",
|
||
" train_freq: Number of steps between each training update.\n",
|
||
" seed: RNG seed.\n",
|
||
"\n",
|
||
" \"\"\"\n",
|
||
" super().__init__(seed, n_actions)\n",
|
||
" self.n_features = n_features\n",
|
||
" self.lr = lr\n",
|
||
" self.gamma = gamma\n",
|
||
" self.batch_size = batch_size\n",
|
||
" self.target_update_freq = target_update_freq\n",
|
||
" self.train_freq = train_freq\n",
|
||
" self.update_step = 0\n",
|
||
" self.train_step = 0\n",
|
||
"\n",
|
||
" torch.manual_seed(seed)\n",
|
||
" self.device = torch.device(\"cpu\")\n",
|
||
" self.q_net = QNetwork(n_features, n_actions).to(self.device)\n",
|
||
" self.target_net = QNetwork(n_features, n_actions).to(self.device)\n",
|
||
" self.target_net.load_state_dict(self.q_net.state_dict())\n",
|
||
" self.target_net.eval()\n",
|
||
"\n",
|
||
" self.optimizer = optim.Adam(self.q_net.parameters(), lr=lr)\n",
|
||
" self.loss_fn = nn.SmoothL1Loss()\n",
|
||
"\n",
|
||
" self.replay_buffer = ReplayBuffer(buffer_size)\n",
|
||
"\n",
|
||
" def get_action(self, observation: np.ndarray, epsilon: float = 0.0) -> int:\n",
|
||
" \"\"\"Select action using epsilon-greedy policy over Q-network outputs.\"\"\"\n",
|
||
" if self.rng.random() < epsilon:\n",
|
||
" return int(self.rng.integers(0, self.action_space))\n",
|
||
"\n",
|
||
" phi = normalize_obs(observation)\n",
|
||
" with torch.no_grad():\n",
|
||
" state_t = torch.from_numpy(phi).float().unsqueeze(0).to(self.device)\n",
|
||
" q_vals = self.q_net(state_t).numpy().squeeze(0)\n",
|
||
" return epsilon_greedy(q_vals, 0.0, self.rng)\n",
|
||
"\n",
|
||
" def update(\n",
|
||
" self,\n",
|
||
" state: np.ndarray,\n",
|
||
" action: int,\n",
|
||
" reward: float,\n",
|
||
" next_state: np.ndarray,\n",
|
||
" done: bool,\n",
|
||
" next_action: int | None = None,\n",
|
||
" agent_id: str = \"single\",\n",
|
||
" ) -> None:\n",
|
||
" \"\"\"Store transition and perform a minibatch DQN update.\"\"\"\n",
|
||
" _ = next_action\n",
|
||
"\n",
|
||
" phi_s = normalize_obs(state)\n",
|
||
" phi_sp = normalize_obs(next_state)\n",
|
||
" self.replay_buffer.push(phi_s, action, reward, phi_sp, done)\n",
|
||
"\n",
|
||
" self.update_step += 1\n",
|
||
" # Optimize: only train every `train_freq` steps to save computation\n",
|
||
" if (\n",
|
||
" len(self.replay_buffer) < self.batch_size\n",
|
||
" or self.update_step % self.train_freq != 0\n",
|
||
" ):\n",
|
||
" return\n",
|
||
"\n",
|
||
" states_b, actions_b, rewards_b, next_states_b, dones_b = (\n",
|
||
" self.replay_buffer.sample(\n",
|
||
" self.batch_size,\n",
|
||
" self.rng,\n",
|
||
" )\n",
|
||
" )\n",
|
||
"\n",
|
||
" states_t = torch.from_numpy(states_b).float().to(self.device)\n",
|
||
" actions_t = torch.from_numpy(actions_b).long().to(self.device)\n",
|
||
" rewards_t = torch.from_numpy(rewards_b).float().to(self.device)\n",
|
||
" next_states_t = torch.from_numpy(next_states_b).float().to(self.device)\n",
|
||
" dones_t = torch.from_numpy(dones_b).float().to(self.device)\n",
|
||
"\n",
|
||
" q_values = self.q_net(states_t)\n",
|
||
" q_curr = q_values.gather(1, actions_t.unsqueeze(1)).squeeze(1)\n",
|
||
"\n",
|
||
" with torch.no_grad():\n",
|
||
" q_next = self.target_net(next_states_t).max(dim=1).values\n",
|
||
" targets = rewards_t + (1.0 - dones_t) * self.gamma * q_next\n",
|
||
"\n",
|
||
" loss = self.loss_fn(q_curr, targets)\n",
|
||
" self.optimizer.zero_grad()\n",
|
||
" loss.backward()\n",
|
||
" nn.utils.clip_grad_norm_(self.q_net.parameters(), max_norm=10.0)\n",
|
||
" self.optimizer.step()\n",
|
||
"\n",
|
||
" self.train_step += 1\n",
|
||
" if self.train_step % self.target_update_freq == 0:\n",
|
||
" self.target_net.load_state_dict(self.q_net.state_dict())\n",
|
||
"\n",
|
||
" def save(self, filename: str) -> None:\n",
|
||
" \"\"\"Save agent state using torch.save (networks + optimizer + metadata).\"\"\"\n",
|
||
" torch.save(\n",
|
||
" {\n",
|
||
" \"q_net\": self.q_net.state_dict(),\n",
|
||
" \"target_net\": self.target_net.state_dict(),\n",
|
||
" \"optimizer\": self.optimizer.state_dict(),\n",
|
||
" \"train_step\": self.train_step,\n",
|
||
" \"n_features\": self.n_features,\n",
|
||
" \"action_space\": self.action_space,\n",
|
||
" \"lr\": self.lr,\n",
|
||
" \"gamma\": self.gamma,\n",
|
||
" \"batch_size\": self.batch_size,\n",
|
||
" \"target_update_freq\": self.target_update_freq,\n",
|
||
" },\n",
|
||
" filename,\n",
|
||
" )\n",
|
||
"\n",
|
||
" def load(self, filename: str) -> None:\n",
|
||
" \"\"\"Load agent state from a torch checkpoint.\"\"\"\n",
|
||
" checkpoint = torch.load(filename, map_location=self.device, weights_only=False)\n",
|
||
" self.q_net.load_state_dict(checkpoint[\"q_net\"])\n",
|
||
" self.target_net.load_state_dict(checkpoint[\"target_net\"])\n",
|
||
" self.train_step = checkpoint.get(\"train_step\", 0)\n",
|
||
" self.optimizer = optim.Adam(self.q_net.parameters(), lr=self.lr)\n",
|
||
" self.optimizer.load_state_dict(checkpoint[\"optimizer\"])\n",
|
||
"\n",
|
||
" buffer_capacity = self.replay_buffer.buffer.maxlen\n",
|
||
" if buffer_capacity is None:\n",
|
||
" buffer_capacity = 50_000\n",
|
||
" self.replay_buffer = ReplayBuffer(buffer_capacity)\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "91e51dc8",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Tennis Environment\n",
|
||
"\n",
|
||
"Creation of the Atari Tennis environment via Gymnasium (`ALE/Tennis-v5`) with standard wrappers:\n",
|
||
"- **Grayscale**: `obs_type=\"grayscale\"` — single-channel observations\n",
|
||
"- **Resize**: `ResizeObservation(84, 84)` — downscale to 84×84\n",
|
||
"- **Frame stack**: `FrameStackObservation(4)` — stack 4 consecutive frames\n",
|
||
"\n",
|
||
"The final observation is an array of shape `(4, 84, 84)`, which flattens to 28,224 features.\n",
|
||
"\n",
|
||
"The agent plays against the **built-in Atari AI opponent**."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 60,
|
||
"id": "13b99a28",
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"def create_env() -> tennis_v3.env:\n",
|
||
" \"\"\"Create a PettingZoo Tennis environment with grayscale, resized, frame-stacked observations.\"\"\"\n",
|
||
" return tennis_v3.env(obs_type=\"ram\")\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "18cb28d8",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Training & Evaluation Infrastructure\n",
|
||
"\n",
|
||
"Functions for training and evaluating agents in the single-agent Gymnasium environment:\n",
|
||
"\n",
|
||
"1. **`train_agent`** — Pre-trains an agent against the built-in AI for a given number of episodes with ε-greedy exploration\n",
|
||
"2. **`plot_training_curves`** — Plots the training reward history (moving average) for all agents"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 61,
|
||
"id": "06b91580",
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"def train_agent(\n",
|
||
" env: tennis_v3.env,\n",
|
||
" agent: Agent,\n",
|
||
" name: str,\n",
|
||
" episodes: int = 5000,\n",
|
||
" epsilon_start: float = 1.0,\n",
|
||
" epsilon_end: float = 0.05,\n",
|
||
" total_decay_steps: int = 500_000,\n",
|
||
" max_steps: int = 5000,\n",
|
||
") -> dict[str, list[float]]:\n",
|
||
" \"\"\"Train the given agent in the environment and return training history.\"\"\"\n",
|
||
" history = {\"avg_rewards\": [], \"abs_rewards\": [], \"lengths\": []}\n",
|
||
" global_step = 0\n",
|
||
" pbar = tqdm(range(episodes), desc=f\"Training {name}\", leave=True)\n",
|
||
"\n",
|
||
" for _ep in pbar:\n",
|
||
" env.reset()\n",
|
||
" last_obs = {}\n",
|
||
" last_action = {}\n",
|
||
" total_reward = {\"first_0\": 0.0, \"second_0\": 0.0}\n",
|
||
" steps_in_episode = 0\n",
|
||
"\n",
|
||
" for step_idx, agent_id in enumerate(env.agent_iter()):\n",
|
||
" if step_idx >= max_steps:\n",
|
||
" break\n",
|
||
"\n",
|
||
" steps_in_episode = step_idx\n",
|
||
" obs, reward, termination, truncation, _info = env.last()\n",
|
||
" done = termination or truncation\n",
|
||
" obs_arr = np.asarray(obs)\n",
|
||
"\n",
|
||
" total_reward[agent_id] += float(reward)\n",
|
||
"\n",
|
||
" epsilon = max(\n",
|
||
" epsilon_end,\n",
|
||
" epsilon_start\n",
|
||
" - global_step / total_decay_steps * (epsilon_start - epsilon_end),\n",
|
||
" )\n",
|
||
"\n",
|
||
" action = None if done else agent.get_action(obs_arr, epsilon=epsilon)\n",
|
||
"\n",
|
||
" if agent_id in last_obs:\n",
|
||
" agent.update(\n",
|
||
" state=last_obs[agent_id],\n",
|
||
" action=last_action[agent_id],\n",
|
||
" reward=float(reward),\n",
|
||
" next_state=obs_arr,\n",
|
||
" done=done,\n",
|
||
" next_action=action,\n",
|
||
" agent_id=agent_id,\n",
|
||
" )\n",
|
||
"\n",
|
||
" if action is not None:\n",
|
||
" last_obs[agent_id] = obs_arr\n",
|
||
" last_action[agent_id] = action\n",
|
||
" global_step += 1\n",
|
||
"\n",
|
||
" env.step(action)\n",
|
||
"\n",
|
||
" history[\"avg_rewards\"].append(\n",
|
||
" (total_reward[\"first_0\"] + total_reward[\"second_0\"]) / 2.0,\n",
|
||
" )\n",
|
||
" history[\"abs_rewards\"].append(abs(total_reward[\"first_0\"]))\n",
|
||
" history[\"lengths\"].append(float(steps_in_episode))\n",
|
||
"\n",
|
||
" recent_window = 50\n",
|
||
" if len(history[\"avg_rewards\"]) >= recent_window:\n",
|
||
" recent_avg = np.mean(history[\"avg_rewards\"][-recent_window:])\n",
|
||
" pbar.set_postfix(\n",
|
||
" avg50=f\"{recent_avg:.1f}\",\n",
|
||
" eps=f\"{epsilon:.3f}\",\n",
|
||
" len=f\"{steps_in_episode}\",\n",
|
||
" steps=f\"{global_step}\",\n",
|
||
" )\n",
|
||
"\n",
|
||
" return history\n",
|
||
"\n",
|
||
"def plot_training_curves(\n",
|
||
" training_histories: dict[str, dict[str, list[float]]],\n",
|
||
" path: str,\n",
|
||
" window: int = 100,\n",
|
||
") -> None:\n",
|
||
" \"\"\"Plot training curves for multiple agents, showing average rewards, reward intensity, and episode lengths.\"\"\"\n",
|
||
" fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(13, 10), sharex=True)\n",
|
||
"\n",
|
||
" for name, data in training_histories.items():\n",
|
||
" color = AGENT_COLORS.get(name, \"#7f8c8d\")\n",
|
||
"\n",
|
||
" rewards = data[\"avg_rewards\"]\n",
|
||
" abs_rewards = data[\"abs_rewards\"]\n",
|
||
" if len(rewards) >= window:\n",
|
||
" ma_rew = np.convolve(rewards, np.ones(window) / window, mode=\"valid\")\n",
|
||
" ma_abs = np.convolve(abs_rewards, np.ones(window) / window, mode=\"valid\")\n",
|
||
" x = np.arange(window - 1, len(rewards))\n",
|
||
"\n",
|
||
" ax1.plot(x, ma_rew, label=f\"{name} (Average)\", color=color, linewidth=2)\n",
|
||
" ax1.plot(\n",
|
||
" x,\n",
|
||
" ma_abs,\n",
|
||
" label=f\"{name} (Intensity)\",\n",
|
||
" color=color,\n",
|
||
" linewidth=1.5,\n",
|
||
" linestyle=\"--\",\n",
|
||
" alpha=0.6,\n",
|
||
" )\n",
|
||
" ax1.fill_between(\n",
|
||
" x,\n",
|
||
" ma_rew - np.std(rewards) * 0.2,\n",
|
||
" ma_rew + np.std(rewards) * 0.2,\n",
|
||
" color=color,\n",
|
||
" alpha=0.1,\n",
|
||
" )\n",
|
||
"\n",
|
||
" lengths = data[\"lengths\"]\n",
|
||
" if len(lengths) >= window:\n",
|
||
" ma_len = np.convolve(lengths, np.ones(window) / window, mode=\"valid\")\n",
|
||
" ax2.plot(x, ma_len, label=name, color=color, linewidth=2)\n",
|
||
" ax2.fill_between(\n",
|
||
" x,\n",
|
||
" ma_len - np.std(lengths) * 0.2,\n",
|
||
" ma_len + np.std(lengths) * 0.2,\n",
|
||
" color=color,\n",
|
||
" alpha=0.1,\n",
|
||
" )\n",
|
||
"\n",
|
||
" ax1.set_ylabel(f\"Reward (MA {window})\", fontsize=12)\n",
|
||
" ax1.set_title(\n",
|
||
" \"Training Rewards & Intensity (Self-Play)\", fontsize=14, fontweight=\"bold\",\n",
|
||
" )\n",
|
||
" ax1.legend(fontsize=9, loc=\"upper left\", ncol=2)\n",
|
||
" ax1.grid(alpha=0.3, linestyle=\"--\")\n",
|
||
" ax1.axhline(y=0, color=\"black\", linewidth=0.8, alpha=0.4)\n",
|
||
"\n",
|
||
" ax2.set_xlabel(\"Episodes\", fontsize=12)\n",
|
||
" ax2.set_ylabel(f\"Steps per Episode (MA {window})\", fontsize=12)\n",
|
||
" ax2.set_title(\n",
|
||
" \"Episode Duration (Stability/Survival)\", fontsize=14, fontweight=\"bold\",\n",
|
||
" )\n",
|
||
" ax2.grid(alpha=0.3, linestyle=\"--\")\n",
|
||
"\n",
|
||
" for ax in [ax1, ax2]:\n",
|
||
" ax.spines[\"top\"].set_visible(False)\n",
|
||
" ax.spines[\"right\"].set_visible(False)\n",
|
||
"\n",
|
||
" fig.tight_layout()\n",
|
||
" plt.savefig(path, dpi=150, bbox_inches=\"tight\")\n",
|
||
" plt.show()\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "9605e9c4",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Agent Instantiation & Incremental Training (One Agent at a Time)\n",
|
||
"\n",
|
||
"**Environment**: `ALE/Tennis-v5` (grayscale, 84×84×4 frames → 28,224 features, 18 actions).\n",
|
||
"\n",
|
||
"**Agents**:\n",
|
||
"- **Random** — random baseline (no training needed)\n",
|
||
"- **SARSA** — linear approximation, semi-gradient TD(0)\n",
|
||
"- **Q-Learning** — linear approximation, off-policy\n",
|
||
"- **Monte Carlo** — first-visit MC with linear weights (⚠️ checkpoint loading issues)\n",
|
||
"- **DQN** — deep Q-network with experience replay and target network (⚠️ `.pt` checkpoint loading issues)\n",
|
||
"\n",
|
||
"**Workflow**:\n",
|
||
"1. Train **one** selected agent (`AGENT_TO_TRAIN`)\n",
|
||
"2. Save its weights to `checkpoints/` (`.pkl` for linear agents, `.pt` for DQN)\n",
|
||
"3. Repeat later for another agent without retraining previous ones\n",
|
||
"4. Load all saved checkpoints before the final evaluation"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 72,
|
||
"id": "6f6ba8df",
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"env = create_env()\n",
|
||
"env.reset()\n",
|
||
"obs, *_ = env.last()\n",
|
||
"\n",
|
||
"n_actions = env.action_space(\"first_0\").n\n",
|
||
"n_features = 128\n",
|
||
"\n",
|
||
"agent_random = RandomAgent(seed=42, action_space=int(n_actions))\n",
|
||
"agent_sarsa = SarsaAgent(n_features=n_features, n_actions=n_actions, alpha=1e-4)\n",
|
||
"agent_q = QLearningAgent(n_features=n_features, n_actions=n_actions, alpha=1e-4)\n",
|
||
"agent_mc = MonteCarloAgent(n_features=n_features, n_actions=n_actions, alpha=1e-4)\n",
|
||
"agent_dqn = DQNAgent(n_features=n_features, n_actions=n_actions)\n",
|
||
"\n",
|
||
"agents = {\n",
|
||
" \"Random\": agent_random,\n",
|
||
" \"SARSA\": agent_sarsa,\n",
|
||
" \"Q-Learning\": agent_q,\n",
|
||
" \"MonteCarlo\": agent_mc,\n",
|
||
" \"DQN\": agent_dqn,\n",
|
||
"}\n",
|
||
"\n",
|
||
"AGENT_COLORS = {\n",
|
||
" \"Random\": \"#95a5a6\",\n",
|
||
" \"SARSA\": \"#3498db\",\n",
|
||
" \"Q-Learning\": \"#e74c3c\",\n",
|
||
" \"MonteCarlo\": \"#2ecc71\",\n",
|
||
" \"DQN\": \"#9b59b6\",\n",
|
||
"}\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 75,
|
||
"id": "4d449701",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Starting training for Q-Learning...\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
"application/vnd.jupyter.widget-view+json": {
|
||
"model_id": "0f0c108ba22041e9a6077cbfcbbd96ed",
|
||
"version_major": 2,
|
||
"version_minor": 0
|
||
},
|
||
"text/plain": [
|
||
"Training Q-Learning: 0%| | 0/10000 [00:00<?, ?it/s]"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
},
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Final average reward for Q-Learning: 0.00\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"AGENT_TO_TRAIN = \"Q-Learning\"\n",
|
||
"EPISODES = 10_000\n",
|
||
"FORCE_RETRAIN = True\n",
|
||
"\n",
|
||
"\n",
|
||
"training_histories = {}\n",
|
||
"agent = agents[AGENT_TO_TRAIN]\n",
|
||
"checkpoint_path = get_path(AGENT_TO_TRAIN)\n",
|
||
"\n",
|
||
"if checkpoint_path.exists() and not FORCE_RETRAIN:\n",
|
||
" agent.load(str(checkpoint_path))\n",
|
||
" training_histories[AGENT_TO_TRAIN] = {\n",
|
||
" \"avg_rewards\": [],\n",
|
||
" \"abs_rewards\": [],\n",
|
||
" \"lengths\": [],\n",
|
||
" }\n",
|
||
" print(f\"Loaded {AGENT_TO_TRAIN} from checkpoint.\")\n",
|
||
"else:\n",
|
||
" print(f\"Starting training for {AGENT_TO_TRAIN}...\")\n",
|
||
"\n",
|
||
" d_steps = 500_000 if AGENT_TO_TRAIN in [\"DQN\", \"MonteCarlo\"] else 1_000_000\n",
|
||
" e_end = 0.05 if AGENT_TO_TRAIN in [\"DQN\", \"MonteCarlo\"] else 0.01\n",
|
||
"\n",
|
||
" training_histories[AGENT_TO_TRAIN] = train_agent(\n",
|
||
" env=env,\n",
|
||
" agent=agent,\n",
|
||
" name=AGENT_TO_TRAIN,\n",
|
||
" episodes=EPISODES,\n",
|
||
" epsilon_start=1.0,\n",
|
||
" epsilon_end=e_end,\n",
|
||
" total_decay_steps=d_steps,\n",
|
||
" max_steps=5000,\n",
|
||
" )\n",
|
||
"\n",
|
||
" agent.save(str(checkpoint_path))\n",
|
||
" rewards = training_histories[AGENT_TO_TRAIN][\"avg_rewards\"]\n",
|
||
" if rewards:\n",
|
||
" avg_val = float(np.mean(rewards[-100:]))\n",
|
||
" print(f\"Final average reward for {AGENT_TO_TRAIN}: {avg_val:.2f}\")\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 76,
|
||
"id": "a13a65df",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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|
||
"text/plain": [
|
||
"<Figure size 1300x1000 with 2 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"plot_training_curves(\n",
|
||
" training_histories,\n",
|
||
" f\"plots/{AGENT_TO_TRAIN}_training_curves.png\",\n",
|
||
" window=100,\n",
|
||
")\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "56959ccd",
|
||
"metadata": {},
|
||
"source": [
|
||
"# Multi-Agent Evaluation & Tournament"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "0698f673",
|
||
"metadata": {},
|
||
"source": [
|
||
"### Loading Checkpoints & Running Evaluation\n",
|
||
"\n",
|
||
"Before evaluation, we load the saved weights for each trained agent from the `checkpoints/` directory. If a checkpoint is missing, the agent will play with its initial weights (zeros), which is effectively random behavior."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 65,
|
||
"id": "5315eb02",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Warning: Missing checkpoint for Random\n",
|
||
"Warning: Missing checkpoint for MonteCarlo\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"for name, agent in agents.items():\n",
|
||
" checkpoint_path = get_path(name)\n",
|
||
" if checkpoint_path.exists():\n",
|
||
" agent.load(str(checkpoint_path))\n",
|
||
" else:\n",
|
||
" print(f\"Warning: Missing checkpoint for {name}\")\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "3047c4b0",
|
||
"metadata": {},
|
||
"source": [
|
||
"After individual pre-training against Atari's built-in AI, we move on to **head-to-head evaluation** between our agents.\n",
|
||
"\n",
|
||
"**PettingZoo Environment**: unlike Gymnasium (single player vs built-in AI), PettingZoo (`tennis_v3`) allows **two Python agents** to play against each other. The same preprocessing wrappers are applied (grayscale, resize to 84×84, 4-frame stacking) via **SuperSuit**.\n",
|
||
"\n",
|
||
"**Match Protocol**: each matchup is played over **two legs** with swapped positions (`first_0` / `second_0`) to eliminate any side-of-court advantage. Results are tallied as wins, losses, and draws."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 66,
|
||
"id": "d04d37e0",
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"def run_match(\n",
|
||
" env: tennis_v3.env,\n",
|
||
" agent_first: Agent,\n",
|
||
" agent_second: Agent,\n",
|
||
" episodes: int = 10,\n",
|
||
" max_steps: int = 4000,\n",
|
||
") -> dict[str, int]:\n",
|
||
" \"\"\"Run head-to-head matches between two agents and count wins/draws.\"\"\"\n",
|
||
" wins = {\"first\": 0, \"second\": 0, \"draw\": 0}\n",
|
||
"\n",
|
||
" for _ep in range(episodes):\n",
|
||
" env.reset()\n",
|
||
" rewards = {\"first_0\": 0.0, \"second_0\": 0.0}\n",
|
||
"\n",
|
||
" for step_idx, agent_id in enumerate(env.agent_iter()):\n",
|
||
" if step_idx >= max_steps:\n",
|
||
" break\n",
|
||
"\n",
|
||
" obs, reward, termination, truncation, _info = env.last()\n",
|
||
" done = termination or truncation\n",
|
||
" rewards[agent_id] += float(reward)\n",
|
||
"\n",
|
||
" if done:\n",
|
||
" action = None\n",
|
||
" else:\n",
|
||
" current_agent = agent_first if agent_id == \"first_0\" else agent_second\n",
|
||
" action = current_agent.get_action(np.asarray(obs), epsilon=0.0)\n",
|
||
"\n",
|
||
" env.step(action)\n",
|
||
"\n",
|
||
" if rewards[\"first_0\"] > rewards[\"second_0\"]:\n",
|
||
" wins[\"first\"] += 1\n",
|
||
" elif rewards[\"second_0\"] > rewards[\"first_0\"]:\n",
|
||
" wins[\"second\"] += 1\n",
|
||
" else:\n",
|
||
" wins[\"draw\"] += 1\n",
|
||
"\n",
|
||
" return wins\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "150e6764",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Evaluation against the Random Agent (Baseline)\n",
|
||
"\n",
|
||
"To quantify whether our agents have actually learned, we first evaluate them against the **Random agent** baseline. A properly trained agent should achieve a **win rate significantly above 50%** against a random opponent.\n",
|
||
"\n",
|
||
"Each agent plays **two legs** (one in each position) for a total of 20 episodes. Only decisive matches (excluding draws) are counted in the win rate calculation."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 67,
|
||
"id": "1b85a88f",
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"def evaluate_vs_random(\n",
|
||
" agents: dict[str, Agent],\n",
|
||
" random_agent_name: str = \"Random\",\n",
|
||
" episodes_per_leg: int = 10,\n",
|
||
") -> dict[str, float]:\n",
|
||
" \"\"\"Evaluate each agent against the specified random agent and compute win rates.\"\"\"\n",
|
||
" win_rates = {}\n",
|
||
" env = create_env()\n",
|
||
" agent_random = agents[random_agent_name]\n",
|
||
"\n",
|
||
" for name, agent in agents.items():\n",
|
||
" if name == random_agent_name:\n",
|
||
" continue\n",
|
||
"\n",
|
||
" leg1 = run_match(env, agent, agent_random, episodes=episodes_per_leg)\n",
|
||
" leg2 = run_match(env, agent_random, agent, episodes=episodes_per_leg)\n",
|
||
"\n",
|
||
" total_wins = leg1[\"first\"] + leg2[\"second\"]\n",
|
||
" total_matches = (episodes_per_leg * 2) - (leg1[\"draw\"] + leg2[\"draw\"])\n",
|
||
"\n",
|
||
" if total_matches == 0:\n",
|
||
" win_rates[name] = 0.5\n",
|
||
" else:\n",
|
||
" win_rates[name] = total_wins / total_matches\n",
|
||
"\n",
|
||
" print(\n",
|
||
" f\"{name} vs {random_agent_name}: {total_wins} wins out of {total_matches} decisive matches (Win rate: {win_rates[name]:.1%})\",\n",
|
||
" )\n",
|
||
"\n",
|
||
" env.close()\n",
|
||
" return win_rates\n",
|
||
"\n",
|
||
"\n",
|
||
"def plot_evaluation_results(\n",
|
||
" random_win_rates: dict[str, float],\n",
|
||
" save_path: str = \"plots/evaluation_results.png\",\n",
|
||
") -> None:\n",
|
||
" \"\"\"Plot evaluation results: bar chart of win rates against Random agent.\"\"\"\n",
|
||
" agent_names = list(random_win_rates.keys())\n",
|
||
" rates_pct = [random_win_rates[n] * 100 for n in agent_names]\n",
|
||
" colors = [AGENT_COLORS.get(n, \"#7f8c8d\") for n in agent_names]\n",
|
||
"\n",
|
||
" fig, ax = plt.subplots(figsize=(8, 6))\n",
|
||
"\n",
|
||
" x = np.arange(len(agent_names))\n",
|
||
" bars = ax.bar(x, rates_pct, color=colors, edgecolor=\"white\", width=0.6)\n",
|
||
"\n",
|
||
" ax.set_xticks(x)\n",
|
||
" ax.set_xticklabels(agent_names, rotation=30, ha=\"right\", fontsize=11)\n",
|
||
" ax.set_ylabel(\"Win Rate (%)\", fontsize=12)\n",
|
||
" ax.set_title(\"Win Rate vs Random Baseline\", fontsize=14, fontweight=\"bold\")\n",
|
||
" ax.set_ylim(0, 110)\n",
|
||
" ax.axhline(\n",
|
||
" y=50,\n",
|
||
" color=\"gray\",\n",
|
||
" linestyle=\"--\",\n",
|
||
" linewidth=1.2,\n",
|
||
" alpha=0.7,\n",
|
||
" label=\"50 % baseline\",\n",
|
||
" )\n",
|
||
" ax.legend(fontsize=10, loc=\"upper right\")\n",
|
||
" ax.grid(axis=\"y\", alpha=0.3, linestyle=\"--\")\n",
|
||
" ax.spines[\"top\"].set_visible(False)\n",
|
||
" ax.spines[\"right\"].set_visible(False)\n",
|
||
"\n",
|
||
" for bar, wr in zip(bars, rates_pct, strict=False):\n",
|
||
" ax.text(\n",
|
||
" bar.get_x() + bar.get_width() / 2,\n",
|
||
" bar.get_height() + 2,\n",
|
||
" f\"{wr:.1f} %\",\n",
|
||
" ha=\"center\",\n",
|
||
" va=\"bottom\",\n",
|
||
" fontsize=10,\n",
|
||
" fontweight=\"bold\",\n",
|
||
" )\n",
|
||
"\n",
|
||
" fig.tight_layout()\n",
|
||
" plt.savefig(save_path, dpi=150, bbox_inches=\"tight\")\n",
|
||
" plt.show()\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 68,
|
||
"id": "a053644e",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Evaluation against the Random agent\n"
|
||
]
|
||
},
|
||
{
|
||
"ename": "ValueError",
|
||
"evalue": "matmul: Input operand 1 has a mismatch in its core dimension 0, with gufunc signature (n?,k),(k,m?)->(n?,m?) (size 128 is different from 28224)",
|
||
"output_type": "error",
|
||
"traceback": [
|
||
"\u001b[31m---------------------------------------------------------------------------\u001b[39m",
|
||
"\u001b[31mValueError\u001b[39m Traceback (most recent call last)",
|
||
"\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[68]\u001b[39m\u001b[32m, line 2\u001b[39m\n\u001b[32m 1\u001b[39m \u001b[38;5;28mprint\u001b[39m(\u001b[33m\"\u001b[39m\u001b[33mEvaluation against the Random agent\u001b[39m\u001b[33m\"\u001b[39m)\n\u001b[32m----> \u001b[39m\u001b[32m2\u001b[39m win_rates_vs_random = \u001b[43mevaluate_vs_random\u001b[49m\u001b[43m(\u001b[49m\n\u001b[32m 3\u001b[39m \u001b[43m \u001b[49m\u001b[43magents\u001b[49m\u001b[43m,\u001b[49m\n\u001b[32m 4\u001b[39m \u001b[43m \u001b[49m\u001b[43mrandom_agent_name\u001b[49m\u001b[43m=\u001b[49m\u001b[33;43m\"\u001b[39;49m\u001b[33;43mRandom\u001b[39;49m\u001b[33;43m\"\u001b[39;49m\u001b[43m,\u001b[49m\n\u001b[32m 5\u001b[39m \u001b[43m \u001b[49m\u001b[43mepisodes_per_leg\u001b[49m\u001b[43m=\u001b[49m\u001b[32;43m10\u001b[39;49m\u001b[43m,\u001b[49m\n\u001b[32m 6\u001b[39m \u001b[43m)\u001b[49m\n",
|
||
"\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[67]\u001b[39m\u001b[32m, line 15\u001b[39m, in \u001b[36mevaluate_vs_random\u001b[39m\u001b[34m(agents, random_agent_name, episodes_per_leg)\u001b[39m\n\u001b[32m 12\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m name == random_agent_name:\n\u001b[32m 13\u001b[39m \u001b[38;5;28;01mcontinue\u001b[39;00m\n\u001b[32m---> \u001b[39m\u001b[32m15\u001b[39m leg1 = \u001b[43mrun_match\u001b[49m\u001b[43m(\u001b[49m\u001b[43menv\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43magent\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43magent_random\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mepisodes\u001b[49m\u001b[43m=\u001b[49m\u001b[43mepisodes_per_leg\u001b[49m\u001b[43m)\u001b[49m\n\u001b[32m 16\u001b[39m leg2 = run_match(env, agent_random, agent, episodes=episodes_per_leg)\n\u001b[32m 18\u001b[39m total_wins = leg1[\u001b[33m\"\u001b[39m\u001b[33mfirst\u001b[39m\u001b[33m\"\u001b[39m] + leg2[\u001b[33m\"\u001b[39m\u001b[33msecond\u001b[39m\u001b[33m\"\u001b[39m]\n",
|
||
"\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[66]\u001b[39m\u001b[32m, line 27\u001b[39m, in \u001b[36mrun_match\u001b[39m\u001b[34m(env, agent_first, agent_second, episodes, max_steps)\u001b[39m\n\u001b[32m 25\u001b[39m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[32m 26\u001b[39m current_agent = agent_first \u001b[38;5;28;01mif\u001b[39;00m agent_id == \u001b[33m\"\u001b[39m\u001b[33mfirst_0\u001b[39m\u001b[33m\"\u001b[39m \u001b[38;5;28;01melse\u001b[39;00m agent_second\n\u001b[32m---> \u001b[39m\u001b[32m27\u001b[39m action = \u001b[43mcurrent_agent\u001b[49m\u001b[43m.\u001b[49m\u001b[43mget_action\u001b[49m\u001b[43m(\u001b[49m\u001b[43mnp\u001b[49m\u001b[43m.\u001b[49m\u001b[43masarray\u001b[49m\u001b[43m(\u001b[49m\u001b[43mobs\u001b[49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mepsilon\u001b[49m\u001b[43m=\u001b[49m\u001b[32;43m0.0\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[32m 29\u001b[39m env.step(action)\n\u001b[32m 31\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m rewards[\u001b[33m\"\u001b[39m\u001b[33mfirst_0\u001b[39m\u001b[33m\"\u001b[39m] > rewards[\u001b[33m\"\u001b[39m\u001b[33msecond_0\u001b[39m\u001b[33m\"\u001b[39m]:\n",
|
||
"\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[56]\u001b[39m\u001b[32m, line 59\u001b[39m, in \u001b[36mSarsaAgent.get_action\u001b[39m\u001b[34m(self, observation, epsilon)\u001b[39m\n\u001b[32m 53\u001b[39m \u001b[38;5;250m\u001b[39m\u001b[33;03m\"\"\"Select action using ε-greedy policy over linear Q-values.\u001b[39;00m\n\u001b[32m 54\u001b[39m \n\u001b[32m 55\u001b[39m \u001b[33;03mSame pattern as Lab 7 SarsaAgent.eps_greedy:\u001b[39;00m\n\u001b[32m 56\u001b[39m \u001b[33;03mcompute q-values for all actions, then apply epsilon_greedy.\u001b[39;00m\n\u001b[32m 57\u001b[39m \u001b[33;03m\"\"\"\u001b[39;00m\n\u001b[32m 58\u001b[39m phi = normalize_obs(observation)\n\u001b[32m---> \u001b[39m\u001b[32m59\u001b[39m q_vals = \u001b[38;5;28;43mself\u001b[39;49m\u001b[43m.\u001b[49m\u001b[43m_q_values\u001b[49m\u001b[43m(\u001b[49m\u001b[43mphi\u001b[49m\u001b[43m)\u001b[49m\n\u001b[32m 60\u001b[39m \u001b[38;5;28;01mreturn\u001b[39;00m epsilon_greedy(q_vals, epsilon, \u001b[38;5;28mself\u001b[39m.rng)\n",
|
||
"\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[56]\u001b[39m\u001b[32m, line 50\u001b[39m, in \u001b[36mSarsaAgent._q_values\u001b[39m\u001b[34m(self, phi)\u001b[39m\n\u001b[32m 37\u001b[39m \u001b[38;5;28;01mdef\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34m_q_values\u001b[39m(\u001b[38;5;28mself\u001b[39m, phi: np.ndarray) -> np.ndarray:\n\u001b[32m 38\u001b[39m \u001b[38;5;250m \u001b[39m\u001b[33;03m\"\"\"Compute Q-values for all actions given feature vector phi(s).\u001b[39;00m\n\u001b[32m 39\u001b[39m \n\u001b[32m 40\u001b[39m \u001b[33;03m Equivalent to Lab 7's self.q(s, a) = self.w[idx].sum()\u001b[39;00m\n\u001b[32m (...)\u001b[39m\u001b[32m 48\u001b[39m \n\u001b[32m 49\u001b[39m \u001b[33;03m \"\"\"\u001b[39;00m\n\u001b[32m---> \u001b[39m\u001b[32m50\u001b[39m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43mself\u001b[39;49m\u001b[43m.\u001b[49m\u001b[43mW\u001b[49m\u001b[43m \u001b[49m\u001b[43m@\u001b[49m\u001b[43m \u001b[49m\u001b[43mphi\u001b[49m\n",
|
||
"\u001b[31mValueError\u001b[39m: matmul: Input operand 1 has a mismatch in its core dimension 0, with gufunc signature (n?,k),(k,m?)->(n?,m?) (size 128 is different from 28224)"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"print(\"Evaluation against the Random agent\")\n",
|
||
"win_rates_vs_random = evaluate_vs_random(\n",
|
||
" agents,\n",
|
||
" random_agent_name=\"Random\",\n",
|
||
" episodes_per_leg=10,\n",
|
||
")\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"id": "5fe97c3d",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"ename": "TypeError",
|
||
"evalue": "'float' object is not subscriptable",
|
||
"output_type": "error",
|
||
"traceback": [
|
||
"\u001b[31m---------------------------------------------------------------------------\u001b[39m",
|
||
"\u001b[31mTypeError\u001b[39m Traceback (most recent call last)",
|
||
"\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[62]\u001b[39m\u001b[32m, line 1\u001b[39m\n\u001b[32m----> \u001b[39m\u001b[32m1\u001b[39m \u001b[43mplot_evaluation_results\u001b[49m\u001b[43m(\u001b[49m\n\u001b[32m 2\u001b[39m \u001b[43m \u001b[49m\u001b[43matari_results\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mwin_rates_vs_random\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43msave_path\u001b[49m\u001b[43m=\u001b[49m\u001b[33;43m\"\u001b[39;49m\u001b[33;43mplots/evaluation_results.png\u001b[39;49m\u001b[33;43m\"\u001b[39;49m\u001b[43m,\u001b[49m\n\u001b[32m 3\u001b[39m \u001b[43m)\u001b[49m\n",
|
||
"\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[61]\u001b[39m\u001b[32m, line 66\u001b[39m, in \u001b[36mplot_evaluation_results\u001b[39m\u001b[34m(atari_results, random_results, save_path)\u001b[39m\n\u001b[32m 63\u001b[39m fig, (ax1, ax2) = plt.subplots(\u001b[32m1\u001b[39m, \u001b[32m2\u001b[39m, figsize=(\u001b[32m14\u001b[39m, \u001b[32m5\u001b[39m))\n\u001b[32m 65\u001b[39m \u001b[38;5;66;03m# --- Left: Average reward vs Atari AI with error bars ---\u001b[39;00m\n\u001b[32m---> \u001b[39m\u001b[32m66\u001b[39m means = [\u001b[43matari_results\u001b[49m\u001b[43m[\u001b[49m\u001b[43mn\u001b[49m\u001b[43m]\u001b[49m\u001b[43m[\u001b[49m\u001b[33;43m\"\u001b[39;49m\u001b[33;43mmean\u001b[39;49m\u001b[33;43m\"\u001b[39;49m\u001b[43m]\u001b[49m \u001b[38;5;28;01mfor\u001b[39;00m n \u001b[38;5;129;01min\u001b[39;00m agent_names]\n\u001b[32m 67\u001b[39m stds = [atari_results[n][\u001b[33m\"\u001b[39m\u001b[33mstd\u001b[39m\u001b[33m\"\u001b[39m] \u001b[38;5;28;01mfor\u001b[39;00m n \u001b[38;5;129;01min\u001b[39;00m agent_names]\n\u001b[32m 68\u001b[39m x = np.arange(\u001b[38;5;28mlen\u001b[39m(agent_names))\n",
|
||
"\u001b[31mTypeError\u001b[39m: 'float' object is not subscriptable"
|
||
]
|
||
},
|
||
{
|
||
"ename": "TypeError",
|
||
"evalue": "'float' object is not subscriptable",
|
||
"output_type": "error",
|
||
"traceback": [
|
||
"\u001b[31m---------------------------------------------------------------------------\u001b[39m",
|
||
"\u001b[31mTypeError\u001b[39m Traceback (most recent call last)",
|
||
"\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[62]\u001b[39m\u001b[32m, line 1\u001b[39m\n\u001b[32m----> \u001b[39m\u001b[32m1\u001b[39m \u001b[43mplot_evaluation_results\u001b[49m\u001b[43m(\u001b[49m\n\u001b[32m 2\u001b[39m \u001b[43m \u001b[49m\u001b[43matari_results\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mwin_rates_vs_random\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43msave_path\u001b[49m\u001b[43m=\u001b[49m\u001b[33;43m\"\u001b[39;49m\u001b[33;43mplots/evaluation_results.png\u001b[39;49m\u001b[33;43m\"\u001b[39;49m\u001b[43m,\u001b[49m\n\u001b[32m 3\u001b[39m \u001b[43m)\u001b[49m\n",
|
||
"\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[61]\u001b[39m\u001b[32m, line 66\u001b[39m, in \u001b[36mplot_evaluation_results\u001b[39m\u001b[34m(atari_results, random_results, save_path)\u001b[39m\n\u001b[32m 63\u001b[39m fig, (ax1, ax2) = plt.subplots(\u001b[32m1\u001b[39m, \u001b[32m2\u001b[39m, figsize=(\u001b[32m14\u001b[39m, \u001b[32m5\u001b[39m))\n\u001b[32m 65\u001b[39m \u001b[38;5;66;03m# --- Left: Average reward vs Atari AI with error bars ---\u001b[39;00m\n\u001b[32m---> \u001b[39m\u001b[32m66\u001b[39m means = [\u001b[43matari_results\u001b[49m\u001b[43m[\u001b[49m\u001b[43mn\u001b[49m\u001b[43m]\u001b[49m\u001b[43m[\u001b[49m\u001b[33;43m\"\u001b[39;49m\u001b[33;43mmean\u001b[39;49m\u001b[33;43m\"\u001b[39;49m\u001b[43m]\u001b[49m \u001b[38;5;28;01mfor\u001b[39;00m n \u001b[38;5;129;01min\u001b[39;00m agent_names]\n\u001b[32m 67\u001b[39m stds = [atari_results[n][\u001b[33m\"\u001b[39m\u001b[33mstd\u001b[39m\u001b[33m\"\u001b[39m] \u001b[38;5;28;01mfor\u001b[39;00m n \u001b[38;5;129;01min\u001b[39;00m agent_names]\n\u001b[32m 68\u001b[39m x = np.arange(\u001b[38;5;28mlen\u001b[39m(agent_names))\n",
|
||
"\u001b[31mTypeError\u001b[39m: 'float' object is not subscriptable"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 1400x500 with 2 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"plot_evaluation_results(\n",
|
||
" win_rates_vs_random,\n",
|
||
" save_path=\"plots/evaluation_results.png\",\n",
|
||
")\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "b9cb30f5",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Full Round-Robin Tournament\n",
|
||
"\n",
|
||
"All agents play a **round-robin tournament** where each pair faces off in both positions (`first_0` / `second_0`).\n",
|
||
"\n",
|
||
"The resulting $n \\times n$ matchup matrix is analyzed with:\n",
|
||
"- **Aggregated ranking**: wins from both positions are combined for each agent\n",
|
||
"- **Binomial significance test** ($H_0: p = 0.5$): determines whether the win rate for each matchup is statistically different from a coin flip"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"id": "4031bde5",
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"def run_all_matchups(\n",
|
||
" agents: dict[str, Agent],\n",
|
||
" episodes_per_leg: int = 20,\n",
|
||
") -> tuple[np.ndarray, list[str]]:\n",
|
||
" \"\"\"Run round-robin matches between all pairs of agents and return the matchup matrix.\"\"\"\n",
|
||
" env = create_env()\n",
|
||
" names = [name for name in agents if name != \"Random\"]\n",
|
||
" n = len(names)\n",
|
||
" matrix = np.full((n, n), np.nan)\n",
|
||
"\n",
|
||
" for i in range(n):\n",
|
||
" for j in range(n):\n",
|
||
" if i == j:\n",
|
||
" continue\n",
|
||
" result = run_match(\n",
|
||
" env,\n",
|
||
" agents[names[i]],\n",
|
||
" agents[names[j]],\n",
|
||
" episodes=episodes_per_leg,\n",
|
||
" )\n",
|
||
" matrix[i, j] = result[\"first\"]\n",
|
||
"\n",
|
||
" env.close()\n",
|
||
" return matrix, names\n",
|
||
"\n",
|
||
"\n",
|
||
"def plot_matchup_matrix(\n",
|
||
" matrix: np.ndarray,\n",
|
||
" agent_names: list[str],\n",
|
||
" episodes_per_leg: int = 20,\n",
|
||
" save_path: str = \"plots/championship_matrix.png\",\n",
|
||
") -> None:\n",
|
||
" \"\"\"Plot the matchup matrix as a heatmap with win counts and percentages.\"\"\"\n",
|
||
" n = len(agent_names)\n",
|
||
" pct_matrix = matrix / episodes_per_leg * 100\n",
|
||
"\n",
|
||
" fig, ax = plt.subplots(figsize=(8, 7))\n",
|
||
" masked = np.ma.array(pct_matrix, mask=np.isnan(pct_matrix))\n",
|
||
" cmap = plt.get_cmap(\"RdYlGn\").copy()\n",
|
||
" cmap.set_bad(color=\"#f0f0f0\")\n",
|
||
"\n",
|
||
" im = ax.imshow(masked, cmap=cmap, vmin=0, vmax=100, aspect=\"equal\")\n",
|
||
"\n",
|
||
" ax.set_xticks(np.arange(n))\n",
|
||
" ax.set_yticks(np.arange(n))\n",
|
||
" ax.set_xticklabels(agent_names, rotation=45, ha=\"right\", fontsize=10)\n",
|
||
" ax.set_yticklabels(agent_names, fontsize=10)\n",
|
||
" ax.set_xlabel(\"Opponent (second_0)\", fontsize=11)\n",
|
||
" ax.set_ylabel(\"Agent (first_0)\", fontsize=11)\n",
|
||
" ax.set_title(\"Championship Matchup Matrix\", fontsize=14, fontweight=\"bold\", pad=12)\n",
|
||
"\n",
|
||
" for i in range(n):\n",
|
||
" for j in range(n):\n",
|
||
" if i == j:\n",
|
||
" ax.text(j, i, \"—\", ha=\"center\", va=\"center\", color=\"#aaa\", fontsize=14)\n",
|
||
" else:\n",
|
||
" wins = int(matrix[i, j])\n",
|
||
" pct = pct_matrix[i, j]\n",
|
||
" txt_color = \"white\" if pct > 70 or pct < 30 else \"black\"\n",
|
||
" ax.text(\n",
|
||
" j,\n",
|
||
" i,\n",
|
||
" f\"{wins}\\n({pct:.0f} %)\",\n",
|
||
" ha=\"center\",\n",
|
||
" va=\"center\",\n",
|
||
" color=txt_color,\n",
|
||
" fontsize=9,\n",
|
||
" fontweight=\"bold\",\n",
|
||
" linespacing=1.4,\n",
|
||
" )\n",
|
||
"\n",
|
||
" cbar = fig.colorbar(im, ax=ax, fraction=0.046, pad=0.04)\n",
|
||
" cbar.set_label(f\"Win Rate (%) — {episodes_per_leg} eps per matchup\", fontsize=10)\n",
|
||
" cbar.set_ticks([0, 25, 50, 75, 100])\n",
|
||
" cbar.set_ticklabels([\"0 %\", \"25 %\", \"50 %\", \"75 %\", \"100 %\"])\n",
|
||
"\n",
|
||
" plt.tight_layout()\n",
|
||
" plt.savefig(save_path, dpi=150, bbox_inches=\"tight\")\n",
|
||
" plt.show()\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"id": "b07b403c",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"ename": "KeyboardInterrupt",
|
||
"evalue": "",
|
||
"output_type": "error",
|
||
"traceback": [
|
||
"\u001b[31m---------------------------------------------------------------------------\u001b[39m",
|
||
"\u001b[31mTypeError\u001b[39m Traceback (most recent call last)",
|
||
"\u001b[36mFile \u001b[39m\u001b[32m~/Workspace/studies/.venv/lib/python3.13/site-packages/supersuit/lambda_wrappers/observation_lambda.py:68\u001b[39m, in \u001b[36maec_observation_lambda._modify_observation\u001b[39m\u001b[34m(self, agent, observation)\u001b[39m\n\u001b[32m 67\u001b[39m \u001b[38;5;28;01mtry\u001b[39;00m:\n\u001b[32m---> \u001b[39m\u001b[32m68\u001b[39m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43mself\u001b[39;49m\u001b[43m.\u001b[49m\u001b[43mchange_observation_fn\u001b[49m\u001b[43m(\u001b[49m\u001b[43mobservation\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mold_obs_space\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43magent\u001b[49m\u001b[43m)\u001b[49m\n\u001b[32m 69\u001b[39m \u001b[38;5;28;01mexcept\u001b[39;00m \u001b[38;5;167;01mTypeError\u001b[39;00m:\n",
|
||
"\u001b[31mTypeError\u001b[39m: basic_obs_wrapper.<locals>.change_obs() takes 2 positional arguments but 3 were given",
|
||
"\nDuring handling of the above exception, another exception occurred:\n",
|
||
"\u001b[31mKeyboardInterrupt\u001b[39m Traceback (most recent call last)",
|
||
"\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[41]\u001b[39m\u001b[32m, line 1\u001b[39m\n\u001b[32m----> \u001b[39m\u001b[32m1\u001b[39m matchup_matrix = \u001b[43mrun_all_matchups\u001b[49m\u001b[43m(\u001b[49m\u001b[43magents\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mepisodes_per_leg\u001b[49m\u001b[43m=\u001b[49m\u001b[32;43m20\u001b[39;49m\u001b[43m)\u001b[49m\n",
|
||
"\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[40]\u001b[39m\u001b[32m, line 19\u001b[39m, in \u001b[36mrun_all_matchups\u001b[39m\u001b[34m(agents, episodes_per_leg)\u001b[39m\n\u001b[32m 17\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m i == j:\n\u001b[32m 18\u001b[39m \u001b[38;5;28;01mcontinue\u001b[39;00m\n\u001b[32m---> \u001b[39m\u001b[32m19\u001b[39m result = \u001b[43mrun_match\u001b[49m\u001b[43m(\u001b[49m\n\u001b[32m 20\u001b[39m \u001b[43m \u001b[49m\u001b[43menv\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43magents\u001b[49m\u001b[43m[\u001b[49m\u001b[43mnames\u001b[49m\u001b[43m[\u001b[49m\u001b[43mi\u001b[49m\u001b[43m]\u001b[49m\u001b[43m]\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43magents\u001b[49m\u001b[43m[\u001b[49m\u001b[43mnames\u001b[49m\u001b[43m[\u001b[49m\u001b[43mj\u001b[49m\u001b[43m]\u001b[49m\u001b[43m]\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mepisodes\u001b[49m\u001b[43m=\u001b[49m\u001b[43mepisodes_per_leg\u001b[49m\u001b[43m,\u001b[49m\n\u001b[32m 21\u001b[39m \u001b[43m \u001b[49m\u001b[43m)\u001b[49m\n\u001b[32m 22\u001b[39m matrix[i, j] = result[\u001b[33m\"\u001b[39m\u001b[33mfirst\u001b[39m\u001b[33m\"\u001b[39m]\n\u001b[32m 24\u001b[39m env.close()\n",
|
||
"\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[28]\u001b[39m\u001b[32m, line 37\u001b[39m, in \u001b[36mrun_match\u001b[39m\u001b[34m(env, agent_first, agent_second, episodes, max_steps)\u001b[39m\n\u001b[32m 34\u001b[39m current_agent = agent_first \u001b[38;5;28;01mif\u001b[39;00m agent_id == \u001b[33m\"\u001b[39m\u001b[33mfirst_0\u001b[39m\u001b[33m\"\u001b[39m \u001b[38;5;28;01melse\u001b[39;00m agent_second\n\u001b[32m 35\u001b[39m action = current_agent.get_action(np.asarray(obs), epsilon=\u001b[32m0.0\u001b[39m)\n\u001b[32m---> \u001b[39m\u001b[32m37\u001b[39m \u001b[43menv\u001b[49m\u001b[43m.\u001b[49m\u001b[43mstep\u001b[49m\u001b[43m(\u001b[49m\u001b[43maction\u001b[49m\u001b[43m)\u001b[49m\n\u001b[32m 39\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m step_idx + \u001b[32m1\u001b[39m >= max_steps:\n\u001b[32m 40\u001b[39m \u001b[38;5;28;01mbreak\u001b[39;00m\n",
|
||
"\u001b[36mFile \u001b[39m\u001b[32m~/Workspace/studies/.venv/lib/python3.13/site-packages/supersuit/utils/base_aec_wrapper.py:46\u001b[39m, in \u001b[36mBaseWrapper.step\u001b[39m\u001b[34m(self, action)\u001b[39m\n\u001b[32m 43\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m (\u001b[38;5;28mself\u001b[39m.terminations[agent] \u001b[38;5;129;01mor\u001b[39;00m \u001b[38;5;28mself\u001b[39m.truncations[agent]):\n\u001b[32m 44\u001b[39m action = \u001b[38;5;28mself\u001b[39m._modify_action(agent, action)\n\u001b[32m---> \u001b[39m\u001b[32m46\u001b[39m \u001b[38;5;28;43msuper\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m.\u001b[49m\u001b[43mstep\u001b[49m\u001b[43m(\u001b[49m\u001b[43maction\u001b[49m\u001b[43m)\u001b[49m\n\u001b[32m 48\u001b[39m \u001b[38;5;28mself\u001b[39m._update_step(\u001b[38;5;28mself\u001b[39m.agent_selection)\n",
|
||
"\u001b[36mFile \u001b[39m\u001b[32m~/Workspace/studies/.venv/lib/python3.13/site-packages/pettingzoo/utils/wrappers/order_enforcing.py:70\u001b[39m, in \u001b[36mOrderEnforcingWrapper.step\u001b[39m\u001b[34m(self, action)\u001b[39m\n\u001b[32m 68\u001b[39m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[32m 69\u001b[39m \u001b[38;5;28mself\u001b[39m._has_updated = \u001b[38;5;28;01mTrue\u001b[39;00m\n\u001b[32m---> \u001b[39m\u001b[32m70\u001b[39m \u001b[38;5;28;43msuper\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m.\u001b[49m\u001b[43mstep\u001b[49m\u001b[43m(\u001b[49m\u001b[43maction\u001b[49m\u001b[43m)\u001b[49m\n",
|
||
"\u001b[36mFile \u001b[39m\u001b[32m~/Workspace/studies/.venv/lib/python3.13/site-packages/pettingzoo/utils/wrappers/base.py:47\u001b[39m, in \u001b[36mBaseWrapper.step\u001b[39m\u001b[34m(self, action)\u001b[39m\n\u001b[32m 46\u001b[39m \u001b[38;5;28;01mdef\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34mstep\u001b[39m(\u001b[38;5;28mself\u001b[39m, action: ActionType) -> \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[32m---> \u001b[39m\u001b[32m47\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[43m.\u001b[49m\u001b[43menv\u001b[49m\u001b[43m.\u001b[49m\u001b[43mstep\u001b[49m\u001b[43m(\u001b[49m\u001b[43maction\u001b[49m\u001b[43m)\u001b[49m\n",
|
||
"\u001b[36mFile \u001b[39m\u001b[32m~/Workspace/studies/.venv/lib/python3.13/site-packages/supersuit/generic_wrappers/utils/shared_wrapper_util.py:69\u001b[39m, in \u001b[36mshared_wrapper_aec.step\u001b[39m\u001b[34m(self, action)\u001b[39m\n\u001b[32m 66\u001b[39m \u001b[38;5;28msuper\u001b[39m().step(action)\n\u001b[32m 67\u001b[39m \u001b[38;5;28mself\u001b[39m.add_modifiers(\u001b[38;5;28mself\u001b[39m.agents)\n\u001b[32m 68\u001b[39m \u001b[38;5;28mself\u001b[39m.modifiers[\u001b[38;5;28mself\u001b[39m.agent_selection].modify_obs(\n\u001b[32m---> \u001b[39m\u001b[32m69\u001b[39m \u001b[38;5;28;43msuper\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m.\u001b[49m\u001b[43mobserve\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[43m.\u001b[49m\u001b[43magent_selection\u001b[49m\u001b[43m)\u001b[49m\n\u001b[32m 70\u001b[39m )\n",
|
||
"\u001b[36mFile \u001b[39m\u001b[32m~/Workspace/studies/.venv/lib/python3.13/site-packages/pettingzoo/utils/wrappers/order_enforcing.py:75\u001b[39m, in \u001b[36mOrderEnforcingWrapper.observe\u001b[39m\u001b[34m(self, agent)\u001b[39m\n\u001b[32m 73\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28mself\u001b[39m._has_reset:\n\u001b[32m 74\u001b[39m EnvLogger.error_observe_before_reset()\n\u001b[32m---> \u001b[39m\u001b[32m75\u001b[39m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43msuper\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m.\u001b[49m\u001b[43mobserve\u001b[49m\u001b[43m(\u001b[49m\u001b[43magent\u001b[49m\u001b[43m)\u001b[49m\n",
|
||
"\u001b[36mFile \u001b[39m\u001b[32m~/Workspace/studies/.venv/lib/python3.13/site-packages/pettingzoo/utils/wrappers/base.py:41\u001b[39m, in \u001b[36mBaseWrapper.observe\u001b[39m\u001b[34m(self, agent)\u001b[39m\n\u001b[32m 40\u001b[39m \u001b[38;5;28;01mdef\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34mobserve\u001b[39m(\u001b[38;5;28mself\u001b[39m, agent: AgentID) -> ObsType | \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[32m---> \u001b[39m\u001b[32m41\u001b[39m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43mself\u001b[39;49m\u001b[43m.\u001b[49m\u001b[43menv\u001b[49m\u001b[43m.\u001b[49m\u001b[43mobserve\u001b[49m\u001b[43m(\u001b[49m\u001b[43magent\u001b[49m\u001b[43m)\u001b[49m\n",
|
||
"\u001b[36mFile \u001b[39m\u001b[32m~/Workspace/studies/.venv/lib/python3.13/site-packages/supersuit/utils/base_aec_wrapper.py:38\u001b[39m, in \u001b[36mBaseWrapper.observe\u001b[39m\u001b[34m(self, agent)\u001b[39m\n\u001b[32m 34\u001b[39m \u001b[38;5;28;01mdef\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34mobserve\u001b[39m(\u001b[38;5;28mself\u001b[39m, agent):\n\u001b[32m 35\u001b[39m obs = \u001b[38;5;28msuper\u001b[39m().observe(\n\u001b[32m 36\u001b[39m agent\n\u001b[32m 37\u001b[39m ) \u001b[38;5;66;03m# problem is in this line, the obs is sometimes a different size from the obs space\u001b[39;00m\n\u001b[32m---> \u001b[39m\u001b[32m38\u001b[39m observation = \u001b[38;5;28;43mself\u001b[39;49m\u001b[43m.\u001b[49m\u001b[43m_modify_observation\u001b[49m\u001b[43m(\u001b[49m\u001b[43magent\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mobs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[32m 39\u001b[39m \u001b[38;5;28;01mreturn\u001b[39;00m observation\n",
|
||
"\u001b[36mFile \u001b[39m\u001b[32m~/Workspace/studies/.venv/lib/python3.13/site-packages/supersuit/lambda_wrappers/observation_lambda.py:70\u001b[39m, in \u001b[36maec_observation_lambda._modify_observation\u001b[39m\u001b[34m(self, agent, observation)\u001b[39m\n\u001b[32m 68\u001b[39m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28mself\u001b[39m.change_observation_fn(observation, old_obs_space, agent)\n\u001b[32m 69\u001b[39m \u001b[38;5;28;01mexcept\u001b[39;00m \u001b[38;5;167;01mTypeError\u001b[39;00m:\n\u001b[32m---> \u001b[39m\u001b[32m70\u001b[39m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43mself\u001b[39;49m\u001b[43m.\u001b[49m\u001b[43mchange_observation_fn\u001b[49m\u001b[43m(\u001b[49m\u001b[43mobservation\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mold_obs_space\u001b[49m\u001b[43m)\u001b[49m\n",
|
||
"\u001b[36mFile \u001b[39m\u001b[32m~/Workspace/studies/.venv/lib/python3.13/site-packages/supersuit/generic_wrappers/basic_wrappers.py:19\u001b[39m, in \u001b[36mbasic_obs_wrapper.<locals>.change_obs\u001b[39m\u001b[34m(obs, obs_space)\u001b[39m\n\u001b[32m 18\u001b[39m \u001b[38;5;28;01mdef\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34mchange_obs\u001b[39m(obs, obs_space):\n\u001b[32m---> \u001b[39m\u001b[32m19\u001b[39m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mmodule\u001b[49m\u001b[43m.\u001b[49m\u001b[43mchange_observation\u001b[49m\u001b[43m(\u001b[49m\u001b[43mobs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mobs_space\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mparam\u001b[49m\u001b[43m)\u001b[49m\n",
|
||
"\u001b[36mFile \u001b[39m\u001b[32m~/Workspace/studies/.venv/lib/python3.13/site-packages/supersuit/utils/basic_transforms/resize.py:21\u001b[39m, in \u001b[36mchange_observation\u001b[39m\u001b[34m(obs, obs_space, resize)\u001b[39m\n\u001b[32m 17\u001b[39m \u001b[38;5;28;01mdef\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34mchange_obs_space\u001b[39m(obs_space, param):\n\u001b[32m 18\u001b[39m \u001b[38;5;28;01mreturn\u001b[39;00m convert_box(\u001b[38;5;28;01mlambda\u001b[39;00m obs: change_observation(obs, obs_space, param), obs_space)\n\u001b[32m---> \u001b[39m\u001b[32m21\u001b[39m \u001b[38;5;28;01mdef\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34mchange_observation\u001b[39m(obs, obs_space, resize):\n\u001b[32m 22\u001b[39m \u001b[38;5;28;01mimport\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34;01mtinyscaler\u001b[39;00m\n\u001b[32m 24\u001b[39m xsize, ysize, linear_interp = resize\n",
|
||
"\u001b[31mKeyboardInterrupt\u001b[39m: "
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"matchup_matrix, tournament_names = run_all_matchups(agents, episodes_per_leg=20)\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": null,
|
||
"id": "9668071a",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"ename": "NameError",
|
||
"evalue": "name 'matchup_matrix' is not defined",
|
||
"output_type": "error",
|
||
"traceback": [
|
||
"\u001b[31m---------------------------------------------------------------------------\u001b[39m",
|
||
"\u001b[31mNameError\u001b[39m Traceback (most recent call last)",
|
||
"\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[42]\u001b[39m\u001b[32m, line 1\u001b[39m\n\u001b[32m----> \u001b[39m\u001b[32m1\u001b[39m plot_matchup_matrix(\u001b[43mmatchup_matrix\u001b[49m, episodes_per_leg=EPISODES_PER_LEG)\n",
|
||
"\u001b[31mNameError\u001b[39m: name 'matchup_matrix' is not defined"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"plot_matchup_matrix(matchup_matrix, tournament_names, episodes_per_leg=20)\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "32c37e5d",
|
||
"metadata": {},
|
||
"source": [
|
||
"# Conclusion\n",
|
||
"\n",
|
||
"This project implemented and compared five Reinforcement Learning agents on Atari Tennis:\n",
|
||
"\n",
|
||
"| Agent | Type | Policy | Update Rule |\n",
|
||
"|-------|------|--------|-------------|\n",
|
||
"| **Random** | Baseline | Uniform random | None |\n",
|
||
"| **SARSA** | TD(0), on-policy | ε-greedy | $W_a \\leftarrow W_a + \\alpha \\cdot (r + \\gamma \\hat{q}(s', a') - \\hat{q}(s, a)) \\cdot \\phi(s)$ |\n",
|
||
"| **Q-Learning** | TD(0), off-policy | ε-greedy | $W_a \\leftarrow W_a + \\alpha \\cdot (r + \\gamma \\max_{a'} \\hat{q}(s', a') - \\hat{q}(s, a)) \\cdot \\phi(s)$ |\n",
|
||
"| **Monte Carlo** | First-visit MC | ε-greedy | $W_a \\leftarrow W_a + \\alpha \\cdot (G_t - \\hat{q}(s, a)) \\cdot \\phi(s)$ |\n",
|
||
"| **DQN** | Deep Q-Network | ε-greedy | Neural network (MLP 256→256) with experience replay and target network |\n",
|
||
"\n",
|
||
"**Architecture**:\n",
|
||
"- **Linear agents** (SARSA, Q-Learning, Monte Carlo): $\\hat{q}(s, a; \\mathbf{W}) = \\mathbf{W}_a^\\top \\phi(s)$ with $\\phi(s) \\in \\mathbb{R}^{28\\,224}$ (4 grayscale 84×84 frames, normalized)\n",
|
||
"- **DQN**: MLP network (28,224 → 256 → 256 → 18) trained with Adam optimizer, Huber loss, and periodic target network sync\n",
|
||
"\n",
|
||
"**Methodology**:\n",
|
||
"1. **Sequential pre-training** of all agents against Atari's built-in AI (3,000 episodes, ε decaying linearly from 1.0 to 0.05 over 500k steps)\n",
|
||
"2. **Evaluation vs Random** to validate learning (expected win rate > 50%)\n",
|
||
"3. **Evaluation vs Atari AI** with per-episode reward statistics (mean ± std) and distributions\n",
|
||
"4. **Full round-robin tournament** via PettingZoo (20 episodes per matchup per position) with statistical significance analysis"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "15f80f84",
|
||
"metadata": {},
|
||
"source": []
|
||
}
|
||
],
|
||
"metadata": {
|
||
"kernelspec": {
|
||
"display_name": "studies (3.13.9)",
|
||
"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
|
||
}
|