reinforce.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
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   "source": [
    "# REINFORCE Monte Carlo\n",
    "\n",
    "This notebook demonstates the simplest policy gradient method, REINFORCE. This is the Monte-Carlo version of REINFORCE, which means the model can only be updated after the episode has terminated. We will be using the Cartpole environment, since episode termination is easy to achieve on this problem. Monte-Carlo algorithms are not well suited to environments that don't provide a straight forward termination path, because they can get stuck in an infinite loop and never complete the first episode, due to not being able to learn during the episode.\n",
    "\n",
    "This is a pure policy gradient approach, which means we will learn the policy function directly and won't be using a value function for criticing the actions (like the actor-critic methods). The policy function in this case is a 3 layer multi-layer perceptron. The algorithm is on-policy, so it starts by generating an episode $S_0, A_0, R_1, ..., S_{T-1}, A_{T-1}, R_T$, following the policy, $\\pi_\\theta$, until the terminal time step $T$. After the episode has completed the policy, $\\pi_\\theta$, learns by updating its weights, $\\theta$, using the following update rule:\n",
    "$$\\theta \\leftarrow \\theta + \\alpha \\nabla_\\theta \\log(\\pi_\\theta(a_t | s_t))G_t $$\n",
    ", where $t$ is the time step, $\\alpha$ is the step size (or learning rate), and $G_t$ is the discounted return from timestep $t$, given by,\n",
    "$$G_t \\leftarrow \\sum_{k=t+1}^{T}\\gamma^{k-t-1}R_k .$$\n",
    "\n",
    "For more information on the REINFORCE Monte Carlo algorithm, see the blog post by Jordi Torres [Policy-Gradient Methods](https://towardsdatascience.com/policy-gradient-methods-104c783251e0), and chapter 13 of [Reinforcement Learning: An Introduction](http://incompleteideas.net/book/RLbook2018.pdf).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import gymnasium as gym\n",
    "import numpy as np\n",
    "from IPython.display import Video\n",
    "import jax\n",
    "import flax.linen as nn\n",
    "from jax import random\n",
    "from jax import grad\n",
    "import jax.numpy as jnp\n",
    "import optax\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Type of environment, options include:\n",
    "# CartPole-v1\n",
    "ENV_TYPE = \"CartPole-v1\"\n",
    "\n",
    "# Save videos from training\n",
    "SAVE_VIDEOS = False\n",
    "VIDEOS_ROOT_DIR = './videos/reinforce/'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create the environment\n",
    "env = gym.make(ENV_TYPE, render_mode=\"rgb_array\")\n",
    "\n",
    "# Number of possible states and actions\n",
    "num_actions = env.action_space.n\n",
    "obs_dims = env.observation_space.shape\n",
    "obs_upper_bounds = env.observation_space.high\n",
    "obs_lower_bounds = env.observation_space.low"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create The Policy "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "An NVIDIA GPU may be present on this machine, but a CUDA-enabled jaxlib is not installed. Falling back to cpu.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\u001b[3m                               _policy_fn Summary                               \u001b[0m\n",
      "┏━━━━━━━━━┳━━━━━━━━━━━━┳━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━━┓\n",
      "┃\u001b[1m \u001b[0m\u001b[1mpath   \u001b[0m\u001b[1m \u001b[0m┃\u001b[1m \u001b[0m\u001b[1mmodule    \u001b[0m\u001b[1m \u001b[0m┃\u001b[1m \u001b[0m\u001b[1minputs      \u001b[0m\u001b[1m \u001b[0m┃\u001b[1m \u001b[0m\u001b[1moutputs     \u001b[0m\u001b[1m \u001b[0m┃\u001b[1m \u001b[0m\u001b[1mparams                 \u001b[0m\u001b[1m \u001b[0m┃\n",
      "┡━━━━━━━━━╇━━━━━━━━━━━━╇━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━━┩\n",
      "│         │ _policy_fn │ \u001b[2mfloat32\u001b[0m[4]   │ \u001b[2mfloat32\u001b[0m[2]   │                         │\n",
      "├─────────┼────────────┼──────────────┼──────────────┼─────────────────────────┤\n",
      "│ Dense_0 │ Dense      │ \u001b[2mfloat32\u001b[0m[4]   │ \u001b[2mfloat32\u001b[0m[256] │ bias: \u001b[2mfloat32\u001b[0m[256]      │\n",
      "│         │            │              │              │ kernel: \u001b[2mfloat32\u001b[0m[4,256]  │\n",
      "│         │            │              │              │                         │\n",
      "│         │            │              │              │ \u001b[1m1,280 \u001b[0m\u001b[1;2m(5.1 KB)\u001b[0m          │\n",
      "├─────────┼────────────┼──────────────┼──────────────┼─────────────────────────┤\n",
      "│ Dense_1 │ Dense      │ \u001b[2mfloat32\u001b[0m[256] │ \u001b[2mfloat32\u001b[0m[64]  │ bias: \u001b[2mfloat32\u001b[0m[64]       │\n",
      "│         │            │              │              │ kernel: \u001b[2mfloat32\u001b[0m[256,64] │\n",
      "│         │            │              │              │                         │\n",
      "│         │            │              │              │ \u001b[1m16,448 \u001b[0m\u001b[1;2m(65.8 KB)\u001b[0m        │\n",
      "├─────────┼────────────┼──────────────┼──────────────┼─────────────────────────┤\n",
      "│ Dense_2 │ Dense      │ \u001b[2mfloat32\u001b[0m[64]  │ \u001b[2mfloat32\u001b[0m[2]   │ bias: \u001b[2mfloat32\u001b[0m[2]        │\n",
      "│         │            │              │              │ kernel: \u001b[2mfloat32\u001b[0m[64,2]   │\n",
      "│         │            │              │              │                         │\n",
      "│         │            │              │              │ \u001b[1m130 \u001b[0m\u001b[1;2m(520 B)\u001b[0m             │\n",
      "├─────────┼────────────┼──────────────┼──────────────┼─────────────────────────┤\n",
      "│\u001b[1m \u001b[0m\u001b[1m       \u001b[0m\u001b[1m \u001b[0m│\u001b[1m \u001b[0m\u001b[1m          \u001b[0m\u001b[1m \u001b[0m│\u001b[1m \u001b[0m\u001b[1m            \u001b[0m\u001b[1m \u001b[0m│\u001b[1m \u001b[0m\u001b[1m       Total\u001b[0m\u001b[1m \u001b[0m│\u001b[1m \u001b[0m\u001b[1m17,858 \u001b[0m\u001b[1;2m(71.4 KB)\u001b[0m\u001b[1m       \u001b[0m\u001b[1m \u001b[0m│\n",
      "└─────────┴────────────┴──────────────┴──────────────┴─────────────────────────┘\n",
      "\u001b[1m                                                                                \u001b[0m\n",
      "\u001b[1m                       Total Parameters: 17,858 \u001b[0m\u001b[1;2m(71.4 KB)\u001b[0m\u001b[1m                       \u001b[0m\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "class _policy_fn(nn.Module):\n",
    "\n",
    "    @nn.compact\n",
    "    def __call__(self, x):\n",
    "        x = nn.Dense(256)(x)\n",
    "        x = jax.nn.relu(x)\n",
    "        x = nn.Dense(64)(x)\n",
    "        x = jax.nn.relu(x)\n",
    "        x = nn.Dense(num_actions)(x)\n",
    "        return jax.nn.softmax(x)\n",
    "\n",
    "# Create the model object\n",
    "policy_fn = _policy_fn()\n",
    "# Display the model details\n",
    "dummy_x, _ = env.reset()\n",
    "rng_key = random.PRNGKey(64)\n",
    "print(policy_fn.tabulate(rng_key, dummy_x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def loss_fn(variables, states, actions, weights):\n",
    "    action_dists = policy_fn.apply(variables, states)\n",
    "    probs = action_dists[jnp.arange(len(actions)), actions]\n",
    "    log_probs = jnp.log(probs)\n",
    "    loss = -(log_probs * weights).mean()\n",
    "    return loss "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Learn The Optimal Action-Value Function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/ubuntu22/repos/reinforcement-learning-algorithms/venv-pre/lib/python3.10/site-packages/gymnasium/wrappers/rendering.py:282: UserWarning: \u001b[33mWARN: Overwriting existing videos at /home/ubuntu22/repos/reinforcement-learning-algorithms/videos/reinforce folder (try specifying a different `video_folder` for the `RecordVideo` wrapper if this is not desired)\u001b[0m\n",
      "  logger.warn(\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Episode 5 Average Returns: 34.60\n",
      "Episode 10 Average Returns: 55.00\n",
      "Episode 15 Average Returns: 80.20\n",
      "Episode 20 Average Returns: 128.60\n",
      "Episode 25 Average Returns: 122.20\n",
      "Episode 30 Average Returns: 96.80\n",
      "Episode 35 Average Returns: 152.40\n",
      "Episode 40 Average Returns: 166.80\n",
      "Episode 45 Average Returns: 254.60\n",
      "Episode 50 Average Returns: 189.60\n"
     ]
    }
   ],
   "source": [
    "# Number of episodes to train on\n",
    "episodes = 53\n",
    "# Sliding window for episode evaluation (needs to be less than episodes)\n",
    "episode_window = 5\n",
    "# Discount ratio\n",
    "gamma = 0.99\n",
    "# Step size\n",
    "alpha = 0.003\n",
    "\n",
    "variables = policy_fn.init(rng_key, dummy_x)\n",
    "\n",
    "optimizer = optax.adam(learning_rate=alpha)\n",
    "opt_state = optimizer.init(variables)\n",
    "\n",
    "env = gym.make(ENV_TYPE, render_mode=\"rgb_array\")\n",
    "env = gym.wrappers.RecordEpisodeStatistics(env, buffer_length=episodes)\n",
    "\n",
    "if SAVE_VIDEOS:\n",
    "    os.makedirs(VIDEOS_ROOT_DIR, exist_ok=True)\n",
    "    env = gym.wrappers.RecordVideo(\n",
    "        env=env, \n",
    "        video_folder=VIDEOS_ROOT_DIR,\n",
    "        episode_trigger=lambda episode: episode % 10 == 0,\n",
    "        video_length=0,\n",
    "        name_prefix=ENV_TYPE,\n",
    "        fps=30\n",
    "        )\n",
    "\n",
    "for episode in range(1, episodes+1):\n",
    "    terminated, truncated = False, False\n",
    "    reward = 0\n",
    "    rewards = []\n",
    "    state, info = env.reset()\n",
    "    states = []\n",
    "    actions = []\n",
    "    # Generate an episode following the policy\n",
    "    while not (terminated or truncated):\n",
    "        states.append(state)\n",
    "        # Select the action following the parametrized policy\n",
    "        action_dist = policy_fn.apply(variables, state)\n",
    "        action_dist = np.array(action_dist).astype(np.float64)\n",
    "        # Divide by the total to ensure the values sum to one\n",
    "        action_dist /= action_dist.sum()\n",
    "        # action = jax.random.choice(rng_key, jnp.arange(num_actions), p=action_dist)\n",
    "        action = np.random.choice(np.arange(num_actions), p=action_dist)\n",
    "        actions.append(action)\n",
    "        # Take the action and observe reward and next state\n",
    "        next_state, reward, terminated, truncated, info = env.step(int(action))\n",
    "        rewards.append(reward)\n",
    "        state = next_state\n",
    "\n",
    "\n",
    "    rewards = jnp.array(rewards)\n",
    "    states = jnp.array(states)\n",
    "    actions = jnp.array(actions)\n",
    "\n",
    "    T = len(states)\n",
    "    weights = []\n",
    "    # Update the policies parameters\n",
    "    for t, state in enumerate(states):\n",
    "        G = 0\n",
    "        for k in range(t, T):\n",
    "            G += (gamma**(k - t)) * rewards[k]\n",
    "        weights.append(G)\n",
    "    weights = jnp.array(weights)\n",
    "\n",
    "    grads = grad(loss_fn, argnums=0)(variables, states, actions, weights)\n",
    "    updates, opt_state = optimizer.update(grads, opt_state, variables)\n",
    "    variables = optax.apply_updates(variables, updates)\n",
    "            \n",
    "\n",
    "    if episode % episode_window == 0:\n",
    "        print(f'Episode {episode} Average Returns: {np.mean(np.array(env.env.return_queue).flatten()[-episode_window:]) :.2f}')"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot The Results\n",
    "\n",
    "For cartpole rewards are assigned for the time spent in a non-terminal state. The episode length and rewards will be identical in this case."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Code used from: https://gymnasium.farama.org/tutorials/blackjack_tutorial/#visualizing-the-training\n",
    "fig, axs = plt.subplots(ncols=2, figsize=(12, 5))\n",
    "axs[0].set_title(\"Episode rewards\")\n",
    "reward_moving_average = (\n",
    "    np.convolve(\n",
    "        np.array(env.env.return_queue).flatten(), np.ones(episode_window), mode=\"valid\"\n",
    "    )\n",
    "    / episode_window\n",
    ")\n",
    "axs[0].plot(range(len(reward_moving_average)), reward_moving_average)\n",
    "axs[1].set_title(\"Episode lengths\")\n",
    "length_moving_average = (\n",
    "    np.convolve(\n",
    "        np.array(env.env.length_queue).flatten(), np.ones(episode_window), mode=\"valid\"\n",
    "    )\n",
    "    / episode_window\n",
    ")\n",
    "axs[1].plot(range(len(length_moving_average)), length_moving_average)\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training Episode Videos"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Episode 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<video src=\"./videos/reinforce//CartPole-v1-episode-0.mp4\" controls  >\n",
       "      Your browser does not support the <code>video</code> element.\n",
       "    </video>"
      ],
      "text/plain": [
       "<IPython.core.display.Video object>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Video(f\"{VIDEOS_ROOT_DIR}/{ENV_TYPE}-episode-0.mp4\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Episode 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<video src=\"./videos/reinforce//CartPole-v1-episode-10.mp4\" controls  >\n",
       "      Your browser does not support the <code>video</code> element.\n",
       "    </video>"
      ],
      "text/plain": [
       "<IPython.core.display.Video object>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Video(f\"{VIDEOS_ROOT_DIR}/{ENV_TYPE}-episode-10.mp4\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Episode 20"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<video src=\"./videos/reinforce//CartPole-v1-episode-20.mp4\" controls  >\n",
       "      Your browser does not support the <code>video</code> element.\n",
       "    </video>"
      ],
      "text/plain": [
       "<IPython.core.display.Video object>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Video(f\"{VIDEOS_ROOT_DIR}/{ENV_TYPE}-episode-20.mp4\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Episode 30"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<video src=\"./videos/reinforce//CartPole-v1-episode-30.mp4\" controls  >\n",
       "      Your browser does not support the <code>video</code> element.\n",
       "    </video>"
      ],
      "text/plain": [
       "<IPython.core.display.Video object>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Video(f\"{VIDEOS_ROOT_DIR}/{ENV_TYPE}-episode-30.mp4\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Episode 40"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<video src=\"./videos/reinforce//CartPole-v1-episode-40.mp4\" controls  >\n",
       "      Your browser does not support the <code>video</code> element.\n",
       "    </video>"
      ],
      "text/plain": [
       "<IPython.core.display.Video object>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Video(f\"{VIDEOS_ROOT_DIR}/{ENV_TYPE}-episode-40.mp4\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Episode 50"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<video src=\"./videos/reinforce//CartPole-v1-episode-50.mp4\" controls  >\n",
       "      Your browser does not support the <code>video</code> element.\n",
       "    </video>"
      ],
      "text/plain": [
       "<IPython.core.display.Video object>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Video(f\"{VIDEOS_ROOT_DIR}/{ENV_TYPE}-episode-50.mp4\")"
   ]
  }
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