2_REINFORCE_continuous.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "m1fDTR8FNJVX"
      },
      "source": [
        "# REINFORCE for continuous action spaces"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Uvj2rXR2f1Kw"
      },
      "outputs": [],
      "source": [
        "!apt-get install -y xvfb\n",
        "\n",
        "!pip install gym==0.23.1 \\\n",
        "    pytorch-lightning==1.6 \\\n",
        "    pyvirtualdisplay\n",
        "\n",
        "!pip install -U brax==0.0.12 jax==0.3.14 jaxlib==0.3.14+cuda11.cudnn82 -f https://storage.googleapis.com/jax-releases/jax_cuda_releases.html\n",
        "\n",
        "\n",
        "import warnings \n",
        "warnings.filterwarnings('ignore')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZOSJl-X7zvs4"
      },
      "source": [
        "#### Setup virtual display"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "B-Z6takfzqGk"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "<pyvirtualdisplay.display.Display at 0x7fbbd8530730>"
            ]
          },
          "execution_count": 1,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "from pyvirtualdisplay import Display\n",
        "Display(visible=False, size=(1400, 900)).start()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Cz8DLleGz_TF"
      },
      "source": [
        "#### Import the necessary code libraries"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "cP5t6U7-nYoc"
      },
      "outputs": [],
      "source": [
        "import copy\n",
        "import torch\n",
        "import random\n",
        "import gym\n",
        "import matplotlib\n",
        "import functools\n",
        "import math\n",
        "\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "import torch.nn.functional as F\n",
        "\n",
        "from collections import deque, namedtuple\n",
        "from IPython.display import HTML\n",
        "from base64 import b64encode\n",
        "\n",
        "from torch import nn\n",
        "from torch.utils.data import DataLoader\n",
        "from torch.utils.data.dataset import IterableDataset\n",
        "from torch.optim import AdamW\n",
        "\n",
        "from torch.distributions import Normal\n",
        "\n",
        "from pytorch_lightning import LightningModule, Trainer\n",
        "\n",
        "import brax.v1\n",
        "from brax.v1 import envs\n",
        "from brax.v1.envs import to_torch\n",
        "from brax.v1.io import html\n",
        "\n",
        "device = 'cuda:0' if torch.cuda.is_available() else 'cpu'\n",
        "num_gpus = torch.cuda.device_count()\n",
        "\n",
        "v = torch.ones(1, device='cuda')"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 25,
      "metadata": {
        "id": "vLpKsS8qPzsN"
      },
      "outputs": [],
      "source": [
        "@torch.no_grad()\n",
        "def plot_policy(policy):\n",
        "  pos = np.linspace(-4.8, 4.8, 100)\n",
        "  vel = np.random.random(size=(10000, 1)) * 0.1\n",
        "  ang = np.linspace(-0.418, 0.418, 100)\n",
        "  ang_vel = np.random.random(size=(10000, 1)) * 0.1\n",
        "\n",
        "  g1, g2 = np.meshgrid(pos, ang)\n",
        "  grid = np.stack((g1,g2), axis=-1)\n",
        "  grid = grid.reshape(-1, 2)\n",
        "  grid = np.hstack((grid, vel, ang_vel))\n",
        "\n",
        "  grid = torch.from_numpy(grid).float()\n",
        "  loc, _ = policy(grid)\n",
        "\n",
        "  plot_vals = loc.numpy()\n",
        "  plot_vals = plot_vals.reshape(100, 100)[::-1]\n",
        "\n",
        "  plt.figure(figsize=(8, 8))\n",
        "  plt.imshow(plot_vals, cmap='coolwarm')\n",
        "  plt.colorbar()\n",
        "  plt.clim(-1, 1)\n",
        "  plt.title(\"P(left | s)\", size=20)\n",
        "  plt.xlabel(\"Cart Position\", size=14)\n",
        "  plt.ylabel(\"Pole angle\", size=14)\n",
        "  plt.xticks(ticks=[0, 50, 100], labels=['-4.8', '0', '4.8'])\n",
        "  plt.yticks(ticks=[100, 50, 0], labels=['-0.418', '0', '0.418'])\n",
        "\n",
        "\n",
        "@torch.no_grad()\n",
        "def create_video(env, episode_length, policy=None):\n",
        "  qp_array = []\n",
        "  state = env.reset()\n",
        "  for i in range(episode_length):\n",
        "    if policy:\n",
        "      loc, scale = policy(state)\n",
        "      sample = torch.normal(loc, scale)\n",
        "      action = torch.tanh(sample)\n",
        "    else:\n",
        "      action = env.action_space.sample()\n",
        "    state, _, _, _ = env.step(action)\n",
        "    qp_array.append(env.unwrapped._state.qp)\n",
        "  return HTML(html.render(env.unwrapped._env.sys, qp_array))\n",
        "\n",
        "\n",
        "@torch.no_grad()\n",
        "def test_agent(env, episode_length, policy, episodes=10):\n",
        "  ep_returns = []\n",
        "  for ep in range(episodes):\n",
        "    state = env.reset()\n",
        "    done = False\n",
        "    ep_ret = 0.0\n",
        "\n",
        "    while not done:\n",
        "      loc, scale = policy(state)\n",
        "      sample = torch.normal(loc, scale)\n",
        "      action = torch.tanh(sample)   \n",
        "      state, reward, done, info = env.step(action)\n",
        "      ep_ret += reward.item()\n",
        "\n",
        "    ep_returns.append(ep_ret)\n",
        "\n",
        "  return sum(ep_returns) / episodes  "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CSsBrSxYIkh8"
      },
      "source": [
        "#### Create the policy"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "id": "7hht5L2bjiNw"
      },
      "outputs": [],
      "source": [
        "class GradientPolicy(nn.Module):\n",
        "\n",
        "  def __init__(self, in_features, out_dims, hidden_size=128):\n",
        "    super().__init__()\n",
        "    self.fc1 = nn.Linear(in_features, hidden_size)\n",
        "    self.fc2 = nn.Linear(hidden_size, hidden_size)\n",
        "    self.fc_mu = nn.Linear(hidden_size, out_dims)\n",
        "    self.fc_std = nn.Linear(hidden_size, out_dims)\n",
        "\n",
        "  def forward(self, x):\n",
        "    x = F.relu(self.fc1(x))\n",
        "    x = F.relu(self.fc2(x))\n",
        "    loc = self.fc_mu(x)\n",
        "    #in the robotics environment that we are going to solve, the possible actions have been normalized to [-1, 1]\n",
        "    #that means the maximal force in one direction will be -1 and maximal force in opposite direction will be -1\n",
        "    #so we have to make sure that the mean of our normal distribution is between -1 and +1\n",
        "    loc = torch.tanh(loc)\n",
        "    scale = self.fc_std(x)\n",
        "    #standard deviation is also known as scale of the distribution\n",
        "    #standard deviation can never be negative, it can always be a positive value\n",
        "    #so we also need a function that can make arbitrary negative values into only positive values\n",
        "    scale = F.softplus(scale) + 0.001#0.001 ensures that our standard deviation doesn't goes to zero\n",
        "    return loc, scale"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "d2EMZSjMIxgr"
      },
      "source": [
        "#### Create the environment"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "id": "t-AI3Jbkr4sA"
      },
      "outputs": [],
      "source": [
        "#In the previous notebook, we used a wrapping class to normalize the values of the observations and the rewards. This time, since we are going to use robotics environments from another library\n",
        "#which is brax, we cannot use those normalization wrappers because they are not adapted to these envrionments. So to make things simple, we have copied the code from the gym library where we normalize\n",
        "#the observations and the rewards and we have adapted to the environments used in this library\n",
        "class RunningMeanStd:\n",
        "    # https://en.wikipedia.org/wiki/Algorithms_for_calculating_variance#Parallel_algorithm\n",
        "    def __init__(self, epsilon=1e-4, shape=()):\n",
        "        self.mean = torch.zeros(shape, dtype=torch.float32).to(device)\n",
        "        self.var = torch.ones(shape, dtype=torch.float32).to(device)\n",
        "        self.count = epsilon\n",
        "\n",
        "    def update(self, x):\n",
        "        batch_mean = torch.mean(x, dim=0)\n",
        "        batch_var = torch.var(x, dim=0)\n",
        "        batch_count = x.shape[0]\n",
        "        self.update_from_moments(batch_mean, batch_var, batch_count)\n",
        "\n",
        "    def update_from_moments(self, batch_mean, batch_var, batch_count):\n",
        "        self.mean, self.var, self.count = update_mean_var_count_from_moments(\n",
        "            self.mean, self.var, self.count, batch_mean, batch_var, batch_count\n",
        "        )\n",
        "\n",
        "\n",
        "def update_mean_var_count_from_moments(\n",
        "    mean, var, count, batch_mean, batch_var, batch_count\n",
        "):\n",
        "    delta = batch_mean - mean\n",
        "    tot_count = count + batch_count\n",
        "\n",
        "    new_mean = mean + delta * batch_count / tot_count\n",
        "    m_a = var * count\n",
        "    m_b = batch_var * batch_count\n",
        "    M2 = m_a + m_b + torch.square(delta) * count * batch_count / tot_count\n",
        "    new_var = M2 / tot_count\n",
        "    new_count = tot_count\n",
        "\n",
        "    return new_mean, new_var, new_count\n",
        "\n",
        "\n",
        "class NormalizeObservation(gym.core.Wrapper):\n",
        "\n",
        "    def __init__(self, env, epsilon=1e-8):\n",
        "        super().__init__(env)\n",
        "        self.num_envs = getattr(env, \"num_envs\", 1)\n",
        "        self.obs_rms = RunningMeanStd(shape=self.observation_space.shape[-1])\n",
        "        self.epsilon = epsilon\n",
        "\n",
        "    def step(self, action):\n",
        "        obs, rews, dones, infos = self.env.step(action)\n",
        "        obs = self.normalize(obs)\n",
        "        return obs, rews, dones, infos\n",
        "\n",
        "    def reset(self, **kwargs):\n",
        "        return_info = kwargs.get(\"return_info\", False)\n",
        "        if return_info:\n",
        "            obs, info = self.env.reset(**kwargs)\n",
        "        else:\n",
        "            obs = self.env.reset(**kwargs)\n",
        "        obs = self.normalize(obs)\n",
        "        if not return_info:\n",
        "            return obs\n",
        "        else:\n",
        "            return obs, info\n",
        "\n",
        "    def normalize(self, obs):\n",
        "        self.obs_rms.update(obs)\n",
        "        return (obs - self.obs_rms.mean) / torch.sqrt(self.obs_rms.var + self.epsilon)\n",
        "\n",
        "\n",
        "class NormalizeReward(gym.core.Wrapper):\n",
        "\n",
        "    def __init__(self, env, gamma=0.99, epsilon=1e-8):\n",
        "        super().__init__(env)\n",
        "        self.num_envs = getattr(env, \"num_envs\", 1)\n",
        "        self.return_rms = RunningMeanStd(shape=())\n",
        "        self.returns = torch.zeros(self.num_envs).to(device)\n",
        "        self.gamma = gamma\n",
        "        self.epsilon = epsilon\n",
        "\n",
        "    def step(self, action):\n",
        "        obs, rews, dones, infos = self.env.step(action)\n",
        "        dones = dones.bool()\n",
        "        self.returns = self.returns * self.gamma + rews\n",
        "        rews = self.normalize(rews)\n",
        "        self.returns[dones] = 0.0\n",
        "        return obs, rews, dones, infos\n",
        "\n",
        "    def normalize(self, rews):\n",
        "        self.return_rms.update(self.returns)\n",
        "        return rews / torch.sqrt(self.return_rms.var + self.epsilon)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "id": "HpD2i_ZSHRmN"
      },
      "outputs": [],
      "source": [
        "#install the environment that we are going to use from the brax library into gym which is our primary reinforcement learning library\n",
        "entry_point = functools.partial(envs.create_gym_env, env_name='inverted_pendulum')\n",
        "gym.register('brax-inverted_pendulum-v0', entry_point=entry_point)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "id": "JX4y_05HHRpD"
      },
      "outputs": [],
      "source": [
        "def create_env(env_name, num_envs=256, episode_length=1000):\n",
        "  env = gym.make(env_name, batch_size=num_envs, episode_length=episode_length)\n",
        "  env = to_torch.JaxToTorchWrapper(env, device=device)\n",
        "  env = NormalizeObservation(env)\n",
        "  env = NormalizeReward(env)\n",
        "  return env"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 35,
      "metadata": {
        "id": "NEVW69uEcjBA"
      },
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "/home/akhters/.local/lib/python3.8/site-packages/gym/utils/passive_env_checker.py:174: UserWarning: \u001b[33mWARN: Future gym versions will require that `Env.reset` can be passed a `seed` instead of using `Env.seed` for resetting the environment random number generator.\u001b[0m\n",
            "  logger.warn(\n",
            "/home/akhters/.local/lib/python3.8/site-packages/gym/utils/passive_env_checker.py:187: UserWarning: \u001b[33mWARN: Future gym versions will require that `Env.reset` can be passed `options` to allow the environment initialisation to be passed additional information.\u001b[0m\n",
            "  logger.warn(\n",
            "/home/akhters/.local/lib/python3.8/site-packages/gym/utils/passive_env_checker.py:195: UserWarning: \u001b[33mWARN: The result returned by `env.reset()` was not a tuple of the form `(obs, info)`, where `obs` is a observation and `info` is a dictionary containing additional information. Actual type: `<class 'jaxlib.xla_extension.ArrayImpl'>`\u001b[0m\n",
            "  logger.warn(\n",
            "/home/akhters/.local/lib/python3.8/site-packages/gym/utils/passive_env_checker.py:219: DeprecationWarning: \u001b[33mWARN: Core environment is written in old step API which returns one bool instead of two. It is recommended to rewrite the environment with new step API. \u001b[0m\n",
            "  logger.deprecation(\n",
            "/home/akhters/.local/lib/python3.8/site-packages/gym/utils/passive_env_checker.py:225: DeprecationWarning: `np.bool8` is a deprecated alias for `np.bool_`.  (Deprecated NumPy 1.24)\n",
            "  if not isinstance(done, (bool, np.bool8)):\n",
            "/home/akhters/.local/lib/python3.8/site-packages/gym/utils/passive_env_checker.py:226: UserWarning: \u001b[33mWARN: Expects `done` signal to be a boolean, actual type: <class 'jaxlib.xla_extension.ArrayImpl'>\u001b[0m\n",
            "  logger.warn(\n",
            "/home/akhters/.local/lib/python3.8/site-packages/gym/utils/passive_env_checker.py:137: UserWarning: \u001b[33mWARN: The obs returned by the `step()` method was expecting a numpy array, actual type: <class 'jaxlib.xla_extension.ArrayImpl'>\u001b[0m\n",
            "  logger.warn(\n",
            "/home/akhters/.local/lib/python3.8/site-packages/gym/spaces/box.py:227: UserWarning: \u001b[33mWARN: Casting input x to numpy array.\u001b[0m\n",
            "  logger.warn(\"Casting input x to numpy array.\")\n",
            "/home/akhters/.local/lib/python3.8/site-packages/gym/utils/passive_env_checker.py:252: UserWarning: \u001b[33mWARN: The reward returned by `step()` must be a float, int, np.integer or np.floating, actual type: <class 'jaxlib.xla_extension.ArrayImpl'>\u001b[0m\n",
            "  logger.warn(\n"
          ]
        }
      ],
      "source": [
        "env = gym.make('brax-inverted_pendulum-v0', episode_length=1000)\n",
        "env = to_torch.JaxToTorchWrapper(env, device=device)\n",
        "hello=create_video(env, 1000)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 36,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/html": [
              "\n",
              "<html>\n",
              "  <head>\n",
              "    <title>brax visualizer</title>\n",
              "    <style>\n",
              "      body {\n",
              "        margin: 0;\n",
              "        padding: 0;\n",
              "      }\n",
              "      #brax-viewer {\n",
              "        margin: 0;\n",
              "        padding: 0;\n",
              "        height: 480px;\n",
              "      }\n",
              "    </style>\n",
              "  </head>\n",
              "  <body>\n",
              "    <script type=\"application/javascript\">\n",
              "    var system = {\"config\": {\"bodies\": [{\"name\": \"cart\", \"colliders\": [{\"rotation\": {\"x\": 90.0, \"z\": 90.0, \"y\": 0.0}, \"capsule\": {\"radius\": 0.1, \"length\": 0.4, \"end\": 0}, \"material\": {\"elasticity\": 0.0, \"friction\": 0.0}, \"color\": \"\", \"hidden\": false, \"noContact\": false}], \"inertia\": {\"x\": 1.0, \"y\": 1.0, \"z\": 1.0}, \"mass\": 10.471975, \"frozen\": {\"position\": {\"y\": 1.0, \"z\": 1.0, \"x\": 0.0}, \"rotation\": {\"x\": 1.0, \"y\": 1.0, \"z\": 1.0}, \"all\": false}}, {\"name\": \"pole\", \"colliders\": [{\"capsule\": {\"radius\": 0.049, \"length\": 0.69800085, \"end\": 0}, \"material\": {\"elasticity\": 0.0, \"friction\": 0.0}, \"color\": \"\", \"hidden\": false, \"noContact\": false}], \"inertia\": {\"x\": 1.0, \"y\": 1.0, \"z\": 1.0}, \"mass\": 5.0185914, \"frozen\": {\"position\": {\"y\": 1.0, \"x\": 0.0, \"z\": 0.0}, \"rotation\": {\"x\": 1.0, \"z\": 1.0, \"y\": 0.0}, \"all\": false}}], \"joints\": [{\"name\": 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[[1.0, 0.0, 0.0, 0.0], [0.9999977350234985, 0.0, -0.0021265007089823484, 0.0]], [[1.0, 0.0, 0.0, 0.0], [0.9999959468841553, 0.0, -0.00287815323099494, 0.0]], [[1.0, 0.0, 0.0, 0.0], [0.9999921321868896, 0.0, -0.00397236505523324, 0.0]], [[1.0, 0.0, 0.0, 0.0], [0.9999588131904602, 0.0, -0.009087157435715199, 0.0]], [[1.0, 0.0, 0.0, 0.0], [0.9998966455459595, 0.0, -0.014382775872945786, 0.0]], [[1.0, 0.0, 0.0, 0.0], [0.9998387098312378, 0.0, -0.01796538755297661, 0.0]], [[1.0, 0.0, 0.0, 0.0], [0.9997735619544983, 0.0, -0.02128208614885807, 0.0]], [[1.0, 0.0, 0.0, 0.0], [0.9996808171272278, 0.0, -0.025266673415899277, 0.0]], [[1.0, 0.0, 0.0, 0.0], [0.9996346831321716, 0.0, -0.027027834206819534, 0.0]], [[1.0, 0.0, 0.0, 0.0], [0.9996639490127563, 0.0, -0.02592330053448677, 0.0]], [[1.0, 0.0, 0.0, 0.0], [0.9996611475944519, 0.0, -0.026033710688352585, 0.0]], [[1.0, 0.0, 0.0, 0.0], [0.9996699094772339, 0.0, -0.02569197490811348, 0.0]], [[1.0, 0.0, 0.0, 0.0], [0.9997334480285645, 0.0, -0.023087045177817345, 0.0]], [[1.0, 0.0, 0.0, 0.0], [0.999830424785614, 0.0, -0.018417464569211006, 0.0]]], \"debug\": false};\n",
              "    </script>\n",
              "    <div id=\"brax-viewer\"></div>\n",
              "    <script type=\"module\">\n",
              "      import {Viewer} from 'https://cdn.jsdelivr.net/gh/google/brax@v0.1.0/js/viewer.js';\n",
              "      const domElement = document.getElementById('brax-viewer');\n",
              "      var viewer = new Viewer(domElement, system);\n",
              "    </script>\n",
              "  </body>\n",
              "</html>\n"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "execution_count": 36,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "hello"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "id": "zEhh8tbITjvt"
      },
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "/home/akhters/.local/lib/python3.8/site-packages/gym/utils/passive_env_checker.py:31: UserWarning: \u001b[33mWARN: A Box observation space has an unconventional shape (neither an image, nor a 1D vector). We recommend flattening the observation to have only a 1D vector or use a custom policy to properly process the data. Actual observation shape: (1, 4)\u001b[0m\n",
            "  logger.warn(\n",
            "/home/akhters/.local/lib/python3.8/site-packages/gym/utils/passive_env_checker.py:174: UserWarning: \u001b[33mWARN: Future gym versions will require that `Env.reset` can be passed a `seed` instead of using `Env.seed` for resetting the environment random number generator.\u001b[0m\n",
            "  logger.warn(\n",
            "/home/akhters/.local/lib/python3.8/site-packages/gym/utils/passive_env_checker.py:187: UserWarning: \u001b[33mWARN: Future gym versions will require that `Env.reset` can be passed `options` to allow the environment initialisation to be passed additional information.\u001b[0m\n",
            "  logger.warn(\n"
          ]
        },
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Num envs:  1 Obs dimentions:  4\n"
          ]
        },
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "/tmp/ipykernel_6429/2546006466.py:13: UserWarning: var(): degrees of freedom is <= 0. Correction should be strictly less than the reduction factor (input numel divided by output numel). (Triggered internally at ../aten/src/ATen/native/ReduceOps.cpp:1807.)\n",
            "  batch_var = torch.var(x, dim=0)\n"
          ]
        }
      ],
      "source": [
        "env = create_env('brax-inverted_pendulum-v0', num_envs=1)\n",
        "obs = env.reset()\n",
        "print(\"Num envs: \", obs.shape[0], \"Obs dimentions: \", obs.shape[1])"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "id": "IADKlcHhhaPj"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "Box(-inf, inf, (1, 4), float32)"
            ]
          },
          "execution_count": 10,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "env.observation_space"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {
        "id": "7WPLsdLwTjyZ"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "Box(-1.0, 1.0, (1, 1), float32)"
            ]
          },
          "execution_count": 11,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "env.action_space"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {
        "id": "k_LlyDyuWFcX"
      },
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "/tmp/ipykernel_6429/2546006466.py:13: UserWarning: var(): degrees of freedom is <= 0. Correction should be strictly less than the reduction factor (input numel divided by output numel). (Triggered internally at ../aten/src/ATen/native/ReduceOps.cpp:1807.)\n",
            "  batch_var = torch.var(x, dim=0)\n"
          ]
        }
      ],
      "source": [
        "obs, reward, done, info = env.step(env.action_space.sample())"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "tensor([[nan, nan, nan, nan]], device='cuda:0')"
            ]
          },
          "execution_count": 13,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "obs"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 14,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "tensor([nan], device='cuda:0')"
            ]
          },
          "execution_count": 14,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "reward"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "tensor([False], device='cuda:0')"
            ]
          },
          "execution_count": 15,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "done"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 16,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "text/plain": [
              "{'first_obs': tensor([[ 0.0000, -0.0013,  0.0000, -0.0041]], device='cuda:0'),\n",
              " 'first_qp': QP(pos=Array([[[ 0.0000000e+00,  0.0000000e+00,  1.0000000e-01],\n",
              "         [-3.9983843e-04,  0.0000000e+00,  3.9999974e-01]]], dtype=float32), rot=Array([[[ 1.0000000e+00,  0.0000000e+00,  0.0000000e+00,  0.0000000e+00],\n",
              "         [ 9.9999976e-01,  0.0000000e+00, -6.6639751e-04,  0.0000000e+00]]],      dtype=float32), vel=Array([[[0., 0., 0.],\n",
              "         [0., 0., 0.]]], dtype=float32), ang=Array([[[0.        , 0.        , 0.        ],\n",
              "         [0.        , 0.00408937, 0.        ]]], dtype=float32)),\n",
              " 'steps': tensor([1.], device='cuda:0'),\n",
              " 'truncation': tensor([0.], device='cuda:0')}"
            ]
          },
          "execution_count": 16,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "info"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": []
    },
    {
      "cell_type": "code",
      "execution_count": 17,
      "metadata": {
        "id": "Vl4GvpJ4Yvl9"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "dict_keys(['first_obs', 'first_qp', 'steps', 'truncation'])"
            ]
          },
          "execution_count": 17,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "info.keys()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "i81fuTi2dCqW"
      },
      "source": [
        "#### Plot the untrained policy"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 18,
      "metadata": {
        "id": "q7viOy02c3pc"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 800x800 with 2 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "policy = GradientPolicy(4, 1)\n",
        "grid = plot_policy(policy)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8hI3qJPwI4Xo"
      },
      "source": [
        "#### Create the dataset"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 19,
      "metadata": {
        "id": "pEJnLgAnV_iR"
      },
      "outputs": [],
      "source": [
        "class RLDataset(IterableDataset):\n",
        "\n",
        "  def __init__(self, env, policy, episode_length, gamma):\n",
        "    self.env = env\n",
        "    self.policy = policy\n",
        "    self.episode_length = episode_length\n",
        "    self.gamma = gamma\n",
        "    self.obs = self.env.reset()\n",
        "  \n",
        "  @torch.no_grad()\n",
        "  def __iter__(self):\n",
        "    transitions = []\n",
        "\n",
        "    for step in range(self.episode_length):\n",
        "      loc, scale = self.policy(self.obs)#for iteration, we are not sending batch inside the network, we are sending single observations of the correct dimension\n",
        "      action = torch.normal(loc, scale)#create a normal distribution for that state, and with that distribution, it select a value according to the distribution probability\n",
        "      next_obs, reward, done, info = self.env.step(action)\n",
        "      transitions.append((self.obs, action, reward, done))\n",
        "      self.obs = next_obs\n",
        "    \n",
        "    obs_b, action_b, reward_b, done_b = map(torch.stack, zip(*transitions))#the observations are already pytorch tensors\n",
        "\n",
        "    running_return = torch.zeros(self.env.num_envs, dtype=torch.float32, device=device)\n",
        "    return_b = torch.zeros_like(reward_b)\n",
        "    #for understanding the following, refer the notebook of the discrete REINFORCE\n",
        "    for row in range(self.episode_length - 1, -1, -1):\n",
        "      running_return = reward_b[row] + ~done_b[row] * self.gamma * running_return\n",
        "      return_b[row] = running_return\n",
        "    \n",
        "    num_samples = self.env.num_envs * self.episode_length\n",
        "    obs_b = obs_b.view(num_samples, -1)\n",
        "    action_b = action_b.view(num_samples, -1)\n",
        "    return_b = return_b.view(num_samples, -1)\n",
        "    \n",
        "    idx = list(range(num_samples))\n",
        "    random.shuffle(idx)\n",
        "\n",
        "    for i in idx:\n",
        "      yield obs_b[i], action_b[i], return_b[i]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jndaQdW1Oklk"
      },
      "source": [
        "#### Create the Proximal Policy Optimization algorithm"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 20,
      "metadata": {
        "id": "by58vmNAV_lP"
      },
      "outputs": [],
      "source": [
        "class reinforce(LightningModule):\n",
        "\n",
        "  def __init__(self, env_name, num_envs=256, episode_length=1_000, batch_size=1024, \n",
        "               hidden_size=64, policy_lr=1e-4, gamma=0.999, entropy_coef=0.0001, optim=AdamW):\n",
        "    \n",
        "    super().__init__()\n",
        "\n",
        "    self.env = create_env(env_name, num_envs=num_envs, episode_length=episode_length)\n",
        "    test_env = gym.make(env_name, episode_length=episode_length)#test_env for testing purposes\n",
        "    test_env = to_torch.JaxToTorchWrapper(test_env, device=device)\n",
        "    self.test_env = NormalizeObservation(test_env)\n",
        "    self.test_env.obs_rms = self.env.obs_rms#to make sure that this test_env observes the same normalized observations as the other one, we are going to share the normalization metrics\n",
        "\n",
        "    obs_size = self.env.observation_space.shape[1]\n",
        "    action_dims = self.env.action_space.shape[1]\n",
        "\n",
        "    self.policy = GradientPolicy(obs_size, action_dims, hidden_size)\n",
        "    self.dataset = RLDataset(self.env, self.policy, episode_length, gamma)\n",
        "\n",
        "    self.save_hyperparameters()\n",
        "    self.videos = []\n",
        "\n",
        "  def configure_optimizers(self):\n",
        "    return self.hparams.optim(self.policy.parameters(), lr=self.hparams.policy_lr)\n",
        " \n",
        "  def train_dataloader(self):\n",
        "    return DataLoader(dataset=self.dataset, batch_size=self.hparams.batch_size)\n",
        "\n",
        "  # Training step.\n",
        "  def training_step(self, batch, batch_idx):\n",
        "    obs, action, returns = batch\n",
        "\n",
        "    loc, scale = self.policy(obs)\n",
        "    dist = Normal(loc, scale)\n",
        "    \n",
        "    log_prob = dist.log_prob(action).sum(dim=-1, keepdim=True)#the way of calculating of log_probabilities is different now, we are calling .log_prob method on the actions takens\n",
        "    #I can't understand, why the .sum() method? we need log of the probability of only the action which was actually taken according to the policy\n",
        "\n",
        "    policy_loss = - log_prob * returns\n",
        "#     The reason for summing the log probabilities across the action dimensions in the line log_prob = dist.log_prob(action).sum(dim=-1, keepdim=True) is related to the nature of the action space and how probabilities are computed for multi-dimensional actions.\n",
        "\n",
        "# Multi-dimensional Actions\n",
        "# In environments where the action space is multi-dimensional (i.e., the agent can take multiple actions at each step), the probability distribution over actions is typically modeled as a product of independent distributions, one for each action dimension. For instance, if the action space is continuous and 3-dimensional, the policy might output 3 separate means and standard deviations, one for each dimension.\n",
        "\n",
        "# Probability of Multi-dimensional Actions\n",
        "# For such multi-dimensional actions, the overall probability of a particular action vector (e.g., \n",
        "# [𝑎1,𝑎2,𝑎3])is the product of the probabilities of the individual action components. In terms of log probabilities:\n",
        "# log𝑃([𝑎1,𝑎2,𝑎3])=log⁡𝑃(𝑎1)+log⁡𝑃(𝑎2)+log⁡𝑃(𝑎3)\n",
        "# So, to get the log probability of the action vector, you sum the log probabilities of the individual actions. This is why the .sum(dim=-1) operation is used.\n",
        "# Example with Code\n",
        "# Let's break down the specific line of code:\n",
        "    entropy = dist.entropy().sum(dim=-1, keepdim=True)\n",
        "# dist.log_prob(action): This computes the log probability of each component of the action vector.\n",
        "# .sum(dim=-1): This sums these log probabilities across the action dimensions, resulting in a single log probability value for the entire action vector.\n",
        "# keepdim=True: This keeps the reduced dimension in the result, which can be useful for maintaining consistent tensor shapes.\n",
        "    self.log(\"episode/Policy Loss\", policy_loss.mean())\n",
        "    self.log(\"episode/Entropy\", entropy.mean())\n",
        "    \n",
        "    return torch.mean(policy_loss - self.hparams.entropy_coef * entropy)\n",
        "\n",
        "  def on_train_epoch_end(self):\n",
        "    if self.current_epoch % 10 == 0:\n",
        "      average_return = test_agent(self.test_env, self.hparams.episode_length, self.policy, episodes=1)\n",
        "      self.log(\"episode/Average Return\", average_return)\n",
        "\n",
        "    if self.current_epoch % 50 == 0:\n",
        "      video = create_video(self.test_env, self.hparams.episode_length, policy=self.policy)\n",
        "      self.videos.append(video)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qeohpzJXRdqr"
      },
      "source": [
        "#### Purge logs and run the visualization tool (Tensorboard)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "QoZw9WYCTB8C"
      },
      "outputs": [],
      "source": [
        "# Start tensorboard.\n",
        "!rm -r /content/lightning_logs/\n",
        "!rm -r /content/videos/\n",
        "%load_ext tensorboard\n",
        "%tensorboard --logdir /content/lightning_logs/"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_zI1Z2TVRh5m"
      },
      "source": [
        "#### Train the policy"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 22,
      "metadata": {
        "id": "r37uP7fJTB-n"
      },
      "outputs": [
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "GPU available: True (cuda), used: True\n",
            "TPU available: False, using: 0 TPU cores\n",
            "HPU available: False, using: 0 HPUs\n",
            "You are using a CUDA device ('NVIDIA GeForce RTX 3060 Laptop GPU') that has Tensor Cores. To properly utilize them, you should set `torch.set_float32_matmul_precision('medium' | 'high')` which will trade-off precision for performance. For more details, read https://pytorch.org/docs/stable/generated/torch.set_float32_matmul_precision.html#torch.set_float32_matmul_precision\n",
            "2024-07-07 21:53:56.589844: W tensorflow/compiler/tf2tensorrt/utils/py_utils.cc:38] TF-TRT Warning: Could not find TensorRT\n",
            "LOCAL_RANK: 0 - CUDA_VISIBLE_DEVICES: [0]\n",
            "\n",
            "  | Name   | Type           | Params | Mode \n",
            "--------------------------------------------------\n",
            "0 | policy | GradientPolicy | 4.6 K  | train\n",
            "--------------------------------------------------\n",
            "4.6 K     Trainable params\n",
            "0         Non-trainable params\n",
            "4.6 K     Total params\n",
            "0.018     Total estimated model params size (MB)\n",
            "/home/akhters/.local/lib/python3.8/site-packages/pytorch_lightning/trainer/connectors/data_connector.py:424: The 'train_dataloader' does not have many workers which may be a bottleneck. Consider increasing the value of the `num_workers` argument` to `num_workers=15` in the `DataLoader` to improve performance.\n",
            "/home/akhters/.local/lib/python3.8/site-packages/gym/utils/passive_env_checker.py:219: DeprecationWarning: \u001b[33mWARN: Core environment is written in old step API which returns one bool instead of two. It is recommended to rewrite the environment with new step API. \u001b[0m\n",
            "  logger.deprecation(\n",
            "/home/akhters/.local/lib/python3.8/site-packages/gym/utils/passive_env_checker.py:225: DeprecationWarning: `np.bool8` is a deprecated alias for `np.bool_`.  (Deprecated NumPy 1.24)\n",
            "  if not isinstance(done, (bool, np.bool8)):\n",
            "/home/akhters/.local/lib/python3.8/site-packages/gym/utils/passive_env_checker.py:226: UserWarning: \u001b[33mWARN: Expects `done` signal to be a boolean, actual type: <class 'jaxlib.xla_extension.ArrayImpl'>\u001b[0m\n",
            "  logger.warn(\n",
            "/home/akhters/.local/lib/python3.8/site-packages/gym/utils/passive_env_checker.py:137: UserWarning: \u001b[33mWARN: The obs returned by the `step()` method was expecting a numpy array, actual type: <class 'jaxlib.xla_extension.ArrayImpl'>\u001b[0m\n",
            "  logger.warn(\n",
            "/home/akhters/.local/lib/python3.8/site-packages/gym/spaces/box.py:227: UserWarning: \u001b[33mWARN: Casting input x to numpy array.\u001b[0m\n",
            "  logger.warn(\"Casting input x to numpy array.\")\n",
            "/home/akhters/.local/lib/python3.8/site-packages/gym/utils/passive_env_checker.py:252: UserWarning: \u001b[33mWARN: The reward returned by `step()` must be a float, int, np.integer or np.floating, actual type: <class 'jaxlib.xla_extension.ArrayImpl'>\u001b[0m\n",
            "  logger.warn(\n"
          ]
        },
        {
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "cbe7ccf29225425caae5464b7d6d37dc",
              "version_major": 2,
              "version_minor": 0
            },
            "text/plain": [
              "Training: |          | 0/? [00:00<?, ?it/s]"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        },
        {
          "name": "stderr",
          "output_type": "stream",
          "text": [
            "/home/akhters/.local/lib/python3.8/site-packages/gym/utils/passive_env_checker.py:174: UserWarning: \u001b[33mWARN: Future gym versions will require that `Env.reset` can be passed a `seed` instead of using `Env.seed` for resetting the environment random number generator.\u001b[0m\n",
            "  logger.warn(\n",
            "/home/akhters/.local/lib/python3.8/site-packages/gym/utils/passive_env_checker.py:187: UserWarning: \u001b[33mWARN: Future gym versions will require that `Env.reset` can be passed `options` to allow the environment initialisation to be passed additional information.\u001b[0m\n",
            "  logger.warn(\n",
            "/home/akhters/.local/lib/python3.8/site-packages/gym/utils/passive_env_checker.py:195: UserWarning: \u001b[33mWARN: The result returned by `env.reset()` was not a tuple of the form `(obs, info)`, where `obs` is a observation and `info` is a dictionary containing additional information. Actual type: `<class 'jaxlib.xla_extension.ArrayImpl'>`\u001b[0m\n",
            "  logger.warn(\n",
            "`Trainer.fit` stopped: `max_epochs=101` reached.\n"
          ]
        }
      ],
      "source": [
        "algo = reinforce('brax-inverted_pendulum-v0')\n",
        "\n",
        "trainer = Trainer(\n",
        "    # gpus=num_gpus,\n",
        "    max_epochs=101,\n",
        "    log_every_n_steps=1)\n",
        "\n",
        "trainer.fit(algo)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 47,
      "metadata": {
        "id": "HewigwoYIWP9"
      },
      "outputs": [
        {
          "data": {
            "text/html": [
              "\n",
              "<html>\n",
              "  <head>\n",
              "    <title>brax visualizer</title>\n",
              "    <style>\n",
              "      body {\n",
              "        margin: 0;\n",
              "        padding: 0;\n",
              "      }\n",
              "      #brax-viewer {\n",
              "        margin: 0;\n",
              "        padding: 0;\n",
              "        height: 480px;\n",
              "      }\n",
              "    </style>\n",
              "  </head>\n",
              "  <body>\n",
              "    <script type=\"application/javascript\">\n",
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