ppo.ipynb

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  "metadata": {
    "colab": {
      "name": "ppo.ipynb",
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "v_Fxb1w7HW62",
        "outputId": "0212058b-03ee-4fe9-bb1d-ce292c265a65"
      },
      "source": [
        "!pip install gym\n",
        "!apt-get install python-opengl -y\n",
        "!apt install xvfb -y\n",
        "!pip install pyvirtualdisplay\n",
        "!pip install piglet\n",
        "!pip install -q git+https://github.com/tensorflow/docs "
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
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            "Requirement already satisfied: future in /usr/local/lib/python3.6/dist-packages (from pyglet<=1.5.0,>=1.4.0->gym) (0.16.0)\n",
            "Reading package lists... Done\n",
            "Building dependency tree       \n",
            "Reading state information... Done\n",
            "Suggested packages:\n",
            "  libgle3\n",
            "The following NEW packages will be installed:\n",
            "  python-opengl\n",
            "0 upgraded, 1 newly installed, 0 to remove and 15 not upgraded.\n",
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            "Get:1 http://archive.ubuntu.com/ubuntu bionic/universe amd64 python-opengl all 3.1.0+dfsg-1 [496 kB]\n",
            "Fetched 496 kB in 1s (473 kB/s)\n",
            "Selecting previously unselected package python-opengl.\n",
            "(Reading database ... 145480 files and directories currently installed.)\n",
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            "Unpacking python-opengl (3.1.0+dfsg-1) ...\n",
            "Setting up python-opengl (3.1.0+dfsg-1) ...\n",
            "Reading package lists... Done\n",
            "Building dependency tree       \n",
            "Reading state information... Done\n",
            "The following NEW packages will be installed:\n",
            "  xvfb\n",
            "0 upgraded, 1 newly installed, 0 to remove and 15 not upgraded.\n",
            "Need to get 784 kB of archives.\n",
            "After this operation, 2,270 kB of additional disk space will be used.\n",
            "Get:1 http://archive.ubuntu.com/ubuntu bionic-updates/universe amd64 xvfb amd64 2:1.19.6-1ubuntu4.8 [784 kB]\n",
            "Fetched 784 kB in 1s (707 kB/s)\n",
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            "(Reading database ... 147835 files and directories currently installed.)\n",
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            "Unpacking xvfb (2:1.19.6-1ubuntu4.8) ...\n",
            "Setting up xvfb (2:1.19.6-1ubuntu4.8) ...\n",
            "Processing triggers for man-db (2.8.3-2ubuntu0.1) ...\n",
            "Collecting pyvirtualdisplay\n",
            "  Downloading https://files.pythonhosted.org/packages/d0/8a/643043cc70791367bee2d19eb20e00ed1a246ac48e5dbe57bbbcc8be40a9/PyVirtualDisplay-1.3.2-py2.py3-none-any.whl\n",
            "Collecting EasyProcess\n",
            "  Downloading https://files.pythonhosted.org/packages/48/3c/75573613641c90c6d094059ac28adb748560d99bd27ee6f80cce398f404e/EasyProcess-0.3-py2.py3-none-any.whl\n",
            "Installing collected packages: EasyProcess, pyvirtualdisplay\n",
            "Successfully installed EasyProcess-0.3 pyvirtualdisplay-1.3.2\n",
            "Collecting piglet\n",
            "  Downloading https://files.pythonhosted.org/packages/11/56/6840e5f45626dc7eb7cd5dff57d11880b3113723b3b7b1fb1fa537855b75/piglet-1.0.0-py2.py3-none-any.whl\n",
            "Collecting piglet-templates\n",
            "\u001b[?25l  Downloading https://files.pythonhosted.org/packages/34/1e/49d7e0df9420eeb13a636487b8e606cf099f2ee0793159edd8ffe905125b/piglet_templates-1.1.0-py3-none-any.whl (63kB)\n",
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            "Collecting Parsley\n",
            "\u001b[?25l  Downloading https://files.pythonhosted.org/packages/2b/d6/4fed8d65e28a970e1c5cb33ce9c7e22e3de745e1b2ae37af051ef16aea3b/Parsley-1.3-py2.py3-none-any.whl (88kB)\n",
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            "Installing collected packages: Parsley, piglet-templates, piglet\n",
            "Successfully installed Parsley-1.3 piglet-1.0.0 piglet-templates-1.1.0\n",
            "\u001b[K     |████████████████████████████████| 1.0MB 9.5MB/s \n",
            "\u001b[?25h  Building wheel for tensorflow-docs (setup.py) ... \u001b[?25l\u001b[?25hdone\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7Va-vLFwFfaq"
      },
      "source": [
        "# Import high level Keras API for tensorflow\n",
        "import tensorflow as tf\n",
        "from tensorflow import keras\n",
        "from tensorflow.keras import layers\n",
        "\n",
        "# Import library for querying for GPU information\n",
        "from tensorflow.python.client import device_lib\n",
        "\n",
        "# Import some utilities for gathering data from a test simulator\n",
        "import gym\n",
        "import numpy as np\n",
        "\n",
        "# Import a progress bar implementation to help track training performance\n",
        "import tqdm\n",
        "\n",
        "# Import plotting utilties for tracking performance over time\n",
        "from matplotlib import pyplot as plt"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XuNAZfRVFldQ"
      },
      "source": [
        "If using Google colab, be sure to enable hardware acceleration by following the instructions at https://colab.research.google.com/notebooks/gpu.ipynb"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jKcLM1R-K1yd"
      },
      "source": [
        "# Make sure that we are using GPUs for now. If we are not, then we should abort.\n",
        "gpus = tf.config.list_physical_devices('GPU')\n",
        "assert(len(gpus) > 0)\n",
        "\n",
        "# TODO #6: It would be good to query for information about the GPU here so that\n",
        "# we can make decisions which allow the code to be portable to devices with\n",
        "# varying amounts of resources.\n",
        "devices_info = device_lib.list_local_devices()\n",
        "gpus_info = [device for device in devices_info if \"GPU\" in device.name]"
      ],
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nC9A-JlbIehX"
      },
      "source": [
        "Next we will define our standard implementation of PPO. For a good overview of how PPO works, there is an excellent resource at https://www.youtube.com/watch?v=5P7I-xPq8u8&t=1s&ab_channel=ArxivInsights\n",
        "\n",
        "The pseudocode from the paper is below:"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YoJ1L7RBPsRM"
      },
      "source": [
        "![ppo-pseudocode.png](data:image/png;base64,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)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PDEMIERsdNoK"
      },
      "source": [
        "We start by creating a an Actor Critic model to build around. The tensorflow documentation has an implementation which has shared hidden layers, allowing for less computation.\n",
        "\n",
        "https://www.tensorflow.org/tutorials/reinforcement_learning/actor_critic"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cHWiz_y6PHk-"
      },
      "source": [
        "# This code is largely from the tensorflow tutorial\n",
        "\n",
        "class SimpleActorCritic(tf.keras.Model):\n",
        "  \"\"\"Combined actor-critic network.\"\"\"\n",
        "\n",
        "  def __init__(self, num_actions, num_hidden_units):\n",
        "    \"\"\"Initialize.\"\"\"\n",
        "    super().__init__()\n",
        "\n",
        "    # Use two dense layers with RELU activations with separate outputs for the\n",
        "    # actor and the critic\n",
        "    self.common1 = layers.Dense(num_hidden_units, activation=\"relu\")\n",
        "    self.common2 = layers.Dense(num_hidden_units, activation=\"relu\")\n",
        "\n",
        "    # The actor is outputting logits for the different possible actions\n",
        "    self.actor = layers.Dense(num_actions)\n",
        "\n",
        "    # The critic is outputting an estimate of the value function\n",
        "    self.critic = layers.Dense(1)\n",
        "\n",
        "  def call(self, inputs):\n",
        "    x1 = self.common1(inputs)\n",
        "    x2 = self.common2(x1)\n",
        "    return self.actor(x2), self.critic(x2)"
      ],
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZtT8cwPEmBZo"
      },
      "source": [
        "Now we have our Actor Critic model which will return an action distribution that we can sample from for our policy as well as a value function estimate for eaach state. For PPO, however, the value function is not sufficient. We need the advantage function. The advantage function is tracking the *advantage* of taking one action over others in a particular state. One high-bias estimate of the advantage function takes in the Q value of that particular state action pair subtracting out the value of being in that state: $A^{\\pi}(s_t,a_t) = Q^{\\pi}(s_t,a_t)-V^{\\pi}(s_t)$. One high-variance estimate of the advantage function takes in the monte carlo returns starting from timestep t: $A^{\\pi}(s_t,a_t) = G_t-V^{\\pi}(s_t)-V^{\\pi}(s_t)$, where $G_t=\\sum^{\\inf}_{n=t}{\\gamma}^{n-t}R_t$ where $R_t$ is the value returned by a reward function $R(s_t, a_t)$.\n",
        "\n",
        "Our actor critic model is already giving us an estimate of the value function $\\hat{V}^{\\pi_{\\theta}}(s_t)$, so now we need to try to choose which variant of advantage function we want to calculate! One approach is to use the lambda return, which is defined in section 12.1 of http://incompleteideas.net/book/RLbook2020.pdf. This estimator provides a formulation of the return which lets us balance between the high-bias Q-value (where $\\lambda=0$) and the high-variance monte carlo return (where $\\lambda=1$). It also lets us factor in the ability to deal with episodes which may be truncated, which in the case of PPO, we have. The formulation of this algorithm, known as TTD($\\lambda$), requires care to ensure its memory requirements scale with the length of the rollouts.  This leaves us with the following equation:\n",
        "$ G^{\\lambda}_{t:t-k}=\\hat{V}^{\\pi_{\\theta}}(s_t)+\\sum^{t+k-1}_{n=t}(\\gamma\\lambda)^{n-t}\\delta'_n$, where $\\delta'_n=R_n+\\gamma\\hat{V}^{\\pi_{\\theta}}(s_{n+1})-\\hat{V}^{\\pi_{\\theta}}(s_{n})$. We can calculate this moving backwards if we have the full rollout up to the end of our truncated episode, where the value of $k$ is determined by where the episode is truncated.\n",
        "\n",
        "The authors of the original PPO paper used exactly this approach, and this estimate of the Advantage function is known as the generalized advantage estimate (GAE)."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tg75UIs6wFR6"
      },
      "source": [
        "def get_expected_returns(values, rewards, final_value, dones, gamma, lambda_):\n",
        "  \"\"\"Compute expected returns per timestep.\"\"\"\n",
        "  # Get the number of rewards to accumulate for the epsiode\n",
        "  n = tf.shape(rewards)[0]\n",
        "\n",
        "  # Initialize values for accumulating the n-step returns\n",
        "  nstep_return = 0\n",
        "  returns = []\n",
        "\n",
        "  # Implement the n-step truncated lambda return, which is described in equation\n",
        "  # 12.10 of http://incompleteideas.net/book/RLbook2020.pdf\n",
        "  # We implement the reverse view, which means working backwards from the end of\n",
        "  # the episode towards the beginning.\n",
        "  for t in tf.range(n - 1, -1, -1):\n",
        "\n",
        "    # We need to take in the value of the next timestep that would have occurred\n",
        "    # after we finished collecting data from our episode. That way, we have a\n",
        "    # value of the state that would have occurred at t+1. This is particularly\n",
        "    # important if the episode had not ended when we stopped gathering data.\n",
        "    next_value = None\n",
        "    if t == n - 1:\n",
        "      next_value = tf.squeeze(final_value, 1)\n",
        "    else:\n",
        "      next_value = values[t + 1]\n",
        "\n",
        "    # Calculate the n-step return delta. Again, we are using the reverse view,\n",
        "    # so we build up the n-step trucated lambda returns backwards. There is a\n",
        "    # good reference in PyTorch over at\n",
        "    # https://github.com/higgsfield/RL-Adventure-2/blob/master/3.ppo.ipynb\n",
        "    nstep_delta = rewards[t] + gamma * next_value * dones[t] - values[t]\n",
        "    nstep_return = nstep_delta + gamma * lambda_ * dones[t] * nstep_return\n",
        "    returns.insert(0, nstep_return + values[t])\n",
        "  \n",
        "  # Convert the list of per-timestep returns into a batched tensor\n",
        "  returns = tf.expand_dims(returns, 0)\n",
        "\n",
        "  return returns"
      ],
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IMQFRcQ1HV-3"
      },
      "source": [
        "Next, we will need to define an implementation of our loss function. The loss function defined in the paper is as follows:"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XSPvRzcEt57b"
      },
      "source": [
        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)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9Mhi1_HJuF3j"
      },
      "source": [
        "In layman's terms, this is basically saying to use a clipping objective, subtract off a scaled down loss of the critic (which in our case is taken from the advantage), and add in a scaled down bonus for an entropy term. We should cover each of these in detail.\n",
        "\n",
        "$L^{CLIP}_t(\\theta)=\\hat{\\mathbb{E}}_t[\\min{(r_t(\\theta)\\hat{A}_t, \\text{clip}(r_t(\\theta),1-\\epsilon,1+\\epsilon))}]$ where $r_t(\\theta)=\\frac{\\pi_\\theta(a_t|s_t)}{\\pi_{\\theta_{old}}(a_t|s_t)}$.\n",
        "\n",
        "This deserves its own deep dive. The term $r_t(\\theta)$ is roughly measuring how a current policy deviates from a previous iteration from the policy. If the two policies are identical, then this value will be exactly 1. The more that the new policy deviates from the old policy, the more different these values will be.\n",
        "\n",
        "The goal is to try and limit deviations from the previous policy to the current policy by trying to limit how large of a step gets taken when the policy change appears to be heading in the right direction. By clipping the loss function in this way, the gradient that gets backpropogated will be conservative if the step taken was in a good direction, but it need not be conservative if the step taken was in a very poor direction from what was present in the original policy. The end result is that the training process tends to be more stable in the policy space.\n",
        "\n",
        "The next two terms in our overall loss function were $-c_1L^{VF}_t(\\theta)+c_2S[\\pi_\\theta](s_t)$. The values $c_1,c_2$ are hyperparameters which control the contribution of the other two terms. The term $L^{VF}_t(\\theta)$ is simply our critic loss, which can be implemented using some standard regression loss formula (the paper uses MSE) for our advantage estimate. The value $S[\\pi_\\theta](s_t)$ is an entropy bonus, where we are essentially trying to maximize the entropy of the distribution of actions for a given state. The generic formula for entropy is $-\\sum p(x)\\log(x)$ for some probability distribution $p(x)$. In this case, our distribution is the policy in a given state, or a sample at some time step of our actor output."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lWYc8rQZaOc_"
      },
      "source": [
        "def compute_ppo_loss(new_action_probs, actions, old_action_probs, values,\n",
        "    advantages, returns, critic_loss_fn, c1, c2, epsilon):\n",
        "  \"\"\"Computes the proximal policy loss.\"\"\"\n",
        "\n",
        "  # Calculate the value of R for the actions taken in our rollouts.\n",
        "  # The log of a product is the sum of the logs, so take the log of the\n",
        "  # action probabilities, subtract what would have been the divisor from what\n",
        "  # would have been the numerator, and then raise back up to the original\n",
        "  # space. This has the same effect as dividing the two.\n",
        "  new_action_log_probs = tf.math.log(new_action_probs)\n",
        "  old_action_log_probs = tf.math.log(old_action_probs)\n",
        "  r = tf.math.exp(new_action_log_probs - old_action_log_probs)\n",
        "\n",
        "  # Calculate the entropy of our new distribution over actions,, which will be\n",
        "  # used to encourage exploration in our actor implementation. Entropy is\n",
        "  # calculated for each sample its distribution of actions, and then the sum of\n",
        "  # entropy over the samples is taken for the loss function.\n",
        "  entropy = -tf.math.reduce_sum(new_action_probs * new_action_log_probs, axis=1)\n",
        "  entropy = tf.math.reduce_mean(entropy)\n",
        "\n",
        "  # Compute the clipped value of r to ensure that we are not too aggressive in\n",
        "  # updates in policy space which we think are going in the right direction. If\n",
        "  # we are going in the wrong direction, feel free to be agressive in going\n",
        "  # back. Perform this over all samples, and take the sum over the samples for\n",
        "  # the loss function.\n",
        "  clipped_r = tf.clip_by_value(r, 1 - epsilon, 1 + epsilon)\n",
        "  actor_loss = tf.math.minimum(r, clipped_r) * advantages\n",
        "  actor_loss = tf.math.reduce_mean(actor_loss)\n",
        "\n",
        "  # We can use any loss function. Use huber loss, which is less sensitive to\n",
        "  # outliers than RMSE and friends.\n",
        "  critic_loss = critic_loss_fn(values, returns)\n",
        "\n",
        "  # Take the negative of our loss because the algorithm is written up for\n",
        "  # ascent, but our optimizer is performing descent\n",
        "  ppo_loss = -(actor_loss - c1 * critic_loss + c2 * entropy)\n",
        "\n",
        "  # Return the components of the the loss function for testing and debugging\n",
        "  # purposes.\n",
        "  return ppo_loss, actor_loss, critic_loss, entropy"
      ],
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cs5q33VK-0Q9"
      },
      "source": [
        "We now have a loss function! We have our actor critic network for the forward and backward pass too. So we are ready to train once we have some data to train on. We can set up a minibatch-based training function in tensorflow.\n",
        "\n",
        "We will gather new predictions for our action distribution and value functions, and we will replay the states from our policy-rollouts as data for our actor critic model. We will need to compare the probability of the selected action in the policy rollout for the new prediction against the old prediction, which is the only slightly tricky part here."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "L7z3p_klBlr6"
      },
      "source": [
        "# Turn on graph execution mode with the tf.function decorator. If debugging is\n",
        "# needed, it might be helpful to comment this decorator out.\n",
        "@tf.function\n",
        "def train_minibatch(mb_states, mb_actions, mb_actions_idx, mb_action_probs,\n",
        "    mb_advantages, mb_returns, model, optimizer, critic_loss_fn, c1, c2,\n",
        "    epsilon):\n",
        "  \"\"\"Runs a model training step.\"\"\"\n",
        "\n",
        "  # Track what we will need to calculate the gradients for with our ActorCritic\n",
        "  # model.\n",
        "  with tf.GradientTape() as tape:\n",
        "    # Predict the new action logits and values given a minibatch of states\n",
        "    new_action_logits, new_values = model(mb_states)\n",
        "\n",
        "    # Calculate new action probabilities from the action logits\n",
        "    new_action_prob_dists = tf.nn.softmax(new_action_logits)\n",
        "\n",
        "    # Get the probability of the chosen actions in a minibatch being taken for\n",
        "    # the new action probability distribution. Then, convert the result into\n",
        "    # a batched tensor.\n",
        "    new_action_probs = tf.gather_nd(new_action_prob_dists, mb_action_idx)\n",
        "    new_action_probs = tf.expand_dims(new_action_probs, 1)\n",
        "\n",
        "    # Calculate the loss values to update our network\n",
        "    loss, L_a, L_c, S = compute_ppo_loss(new_action_probs, mb_actions,\n",
        "        mb_action_probs, new_values, mb_advantages, mb_returns, critic_loss_fn,\n",
        "        c1, c2, epsilon)\n",
        "\n",
        "  # Compute the gradients from the loss\n",
        "  grads = tape.gradient(loss, model.trainable_variables)\n",
        "\n",
        "  # Apply the gradients to the actor critic model's parameters\n",
        "  optimizer.apply_gradients(zip(grads, model.trainable_variables))\n",
        "\n",
        "  return loss, L_a, L_c, S"
      ],
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PvRmzltjCdvJ"
      },
      "source": [
        "At this point, we have our loss function implemented, we have our training loop implemented, and we have a way to get our advantage estimate. We need to set up some hyper-parameters for our test of PPO. Read the next code block to understand how these parameters are used."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uDwQFlZK4vog"
      },
      "source": [
        "################################################################################\n",
        "# Set up the hyper-parameters\n",
        "################################################################################\n",
        "\n",
        "# How many episodes should we gather and train on before we stop training.\n",
        "max_episodes = 5000\n",
        "\n",
        "# When gathering training data, what is the maximum horizon we should look out\n",
        "# over before truncating the episode.\n",
        "max_steps_per_episode = 500\n",
        "\n",
        "# Learning rate for optimizer\n",
        "_learning_rate = 3e-5\n",
        "\n",
        "# Discount factor for future rewards\n",
        "gamma = 0.99\n",
        "\n",
        "# Generalized advantage estimate trade-off (between 0 and 1)\n",
        "lambda_ = 0.97\n",
        "\n",
        "## PPO loss function parameters\n",
        "\n",
        "# Critic loss scaling factor\n",
        "c1 = 0.5\n",
        "\n",
        "# Entropy bonus scaling factor\n",
        "c2 = 1e-3\n",
        "\n",
        "# Actor clipping value\n",
        "epsilon = 0.1\n",
        "\n",
        "# How many episodes should be gathered before an iteration of training\n",
        "gather_episodes = 4\n",
        "\n",
        "# How many training epochs should be run over the gathered data\n",
        "num_epochs = 4\n",
        "\n",
        "# TODO #6: provide constraints on this value based on the architecture\n",
        "# How many training examples are part of a training minibatch\n",
        "minibatch_size = 32\n",
        "\n",
        "################################################################################\n",
        "# Validate hyper-parameters that depend on one another\n",
        "################################################################################\n",
        "\n",
        "# Make sure that the number of training epochs is smaller\n",
        "# than the number of time steps gathered. Since we don't have an actual\n",
        "# number of timesteps gathered, just make a conservative estimate of 5 steps\n",
        "# per episode\n",
        "assert(num_epochs <= (gather_episodes * max_steps_per_episode))"
      ],
      "execution_count": 8,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BivjgeKTHC_3"
      },
      "source": [
        "At long last, we are ready to set up an environment and try things out! Let's start out with a simple Cartpole environment to see how we do.\n",
        "\n",
        "We will iterate over PPO by first gathering a dataset by first running some number of episodes either to completion or truncated to some maximum number of steps per episode. Then, we will perform training of an actor critic model for some number of epochs over the gathered dataset. Then, we repeat the process, using the updated actor critic model to gather data from our latest policy.\n",
        "\n",
        "Once again, it helps to look at the algorithm from the paper:"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jdBS1HAtD2Xl"
      },
      "source": [
        "![ppo-pseudocode.png](data:image/png;base64,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)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vqGcJzp1D7HB"
      },
      "source": [
        "We will also gather episodic rewards and some parameters related to our loss function.\n",
        "\n",
        "It is important to look at the loss not only for understanding how our agent is doing, but also to enable us to perform early stopping to avoid overfitting.\n",
        "\n",
        "It is not critical to gather loss data over time, but this does help us perform analysis of how our training is going. For example, we will be able to look at things like whether training for our model appears to have diverged, or if some component of our loss appears to be specifically misbehaving relative to the others."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "l3W3rMgwH1Zm",
        "outputId": "e13b8c3e-3d48-4e3e-d920-8cf094345701"
      },
      "source": [
        "# Create the environment\n",
        "env = gym.make(\"CartPole-v1\")\n",
        "\n",
        "# Set seed for experiment reproducibility\n",
        "seed = 12345\n",
        "env.seed(seed)\n",
        "tf.random.set_seed(seed)\n",
        "np.random.seed(seed)\n",
        "\n",
        "# Cartpole-v1 is considered solved if average reward is >= 195 over 100 \n",
        "# consecutive trials\n",
        "reward_threshold = 195\n",
        "running_reward = 0\n",
        "\n",
        "## Initialize the actor critic mode\n",
        "\n",
        "# Use the Adam optimizer, which the paper claimed to help speed things up\n",
        "optimizer = tf.keras.optimizers.Adam(learning_rate=_learning_rate)\n",
        "\n",
        "# Use huber loss, which is more stable to outliers than RMSE.\n",
        "critic_loss_fn = tf.keras.losses.MeanSquaredError()\n",
        "\n",
        "# Create the network based on the desired number of action logits and the\n",
        "# desired width of the hidden layers.\n",
        "num_actions = env.action_space.n \n",
        "num_hidden_units = 128\n",
        "model = SimpleActorCritic(num_actions, num_hidden_units)\n",
        "\n",
        "# Initialize values for tracking rewards per episode for the purposes of early\n",
        "# stopping and debugging\n",
        "running_reward = 0\n",
        "max_running_reward = 0\n",
        "episode_rewards = []\n",
        "\n",
        "# Track loss parameters for analysis and debugging\n",
        "total_losses = []\n",
        "actor_losses = []\n",
        "critic_losses = []\n",
        "entropy_terms = []\n",
        "\n",
        "# Use a progress bar to track how far along we are in training.\n",
        "with tqdm.trange(max_episodes // gather_episodes) as steps:\n",
        "  for step in steps:\n",
        "    # Reset training memory for this step of PPO.\n",
        "    states = []\n",
        "    actions = []\n",
        "    action_probs = []\n",
        "    values = []\n",
        "    rewards = []\n",
        "    dones = []\n",
        "\n",
        "    # Gather data over some number of episodes\n",
        "    for g in range(gather_episodes):\n",
        "      # Reset the simulator and episode-tracking metadata\n",
        "      state = env.reset()\n",
        "      done = False\n",
        "      episode_reward = 0\n",
        "      epsiode_returns = []\n",
        "      cur_ep_rewards = []\n",
        "      cur_ep_dones = []\n",
        "\n",
        "      for t in range(max_steps_per_episode):\n",
        "        # Get a logits for actions and predicted value of the state\n",
        "        action_logits, value = model(tf.expand_dims(state, 0))\n",
        "\n",
        "        # Sample an action from the logits. This is coming from a batched\n",
        "        # tensor, but it should only have a single value at index 0,0.\n",
        "        action = tf.random.categorical(action_logits, 1)[0, 0]\n",
        "\n",
        "        # Track the distribution and grad the probability for the action we took\n",
        "        action_prob_dist = tf.nn.softmax(action_logits)\n",
        "        action_prob = action_prob_dist[:, action]\n",
        "\n",
        "        # Take a step in the simulator given our selected action\n",
        "        state, reward, done, _ = env.step(action.numpy())\n",
        "\n",
        "        # Keep track of values when the episode is not done by\n",
        "        # 1 means the timestep counts\n",
        "        done_f = float(1 - int(done))\n",
        "\n",
        "        # Store step result in memory for the multi-episode data set\n",
        "        states.append(state)\n",
        "        actions.append(action)\n",
        "        action_probs.append(action_prob)\n",
        "        values.append(value)\n",
        "        rewards.append(reward)\n",
        "        dones.append(done_f)\n",
        "\n",
        "        # Track cumulative rewards for this episode\n",
        "        cur_ep_rewards.append(reward)\n",
        "        cur_ep_dones.append(done_f)\n",
        "\n",
        "        # If the simulator reports the episode is done, then stop gathering\n",
        "        # data for this episode.\n",
        "        if done:\n",
        "          break\n",
        "\n",
        "      # Keep track of some data related to rewards for early stopping,\n",
        "      # debugging, and analysis purposes.\n",
        "      for reward, done in zip(cur_ep_rewards, cur_ep_dones):\n",
        "        episode_reward += (reward * done)\n",
        "\n",
        "      episode_rewards.append(episode_reward)\n",
        "      running_reward = episode_reward*0.01 + running_reward*.99\n",
        "      max_running_reward = max(running_reward, max_running_reward)\n",
        "\n",
        "    # Convert the data to tensors\n",
        "    states = tf.squeeze(tf.convert_to_tensor(states))\n",
        "    actions = tf.expand_dims(tf.squeeze(tf.convert_to_tensor(actions,\n",
        "        dtype=tf.int32)), 1)\n",
        "    action_probs = tf.expand_dims(tf.squeeze(\n",
        "        tf.convert_to_tensor(action_probs)), 1)\n",
        "    values = tf.expand_dims(tf.squeeze(tf.convert_to_tensor(values)), 1)\n",
        "    rewards = tf.expand_dims(tf.squeeze(tf.convert_to_tensor(rewards)), 1)\n",
        "    dones = tf.expand_dims(tf.squeeze(tf.convert_to_tensor(dones)), 1)\n",
        "\n",
        "    # Get the value of the state one timestep into the future, which is needed\n",
        "    # to calculate the estimate of the return at the last timestep.\n",
        "    _, final_value = model(tf.expand_dims(states[-1], 0))\n",
        "\n",
        "    # Calculate the returns for each timestep, and convert it into a batched\n",
        "    # tensor.\n",
        "    returns = get_expected_returns(values, rewards, final_value, dones, gamma,\n",
        "        lambda_)\n",
        "    returns = tf.expand_dims(tf.squeeze(tf.convert_to_tensor(returns)), 1)\n",
        "\n",
        "    # Calculate the advantage from the estimated returns and the predicted\n",
        "    # values for the model used to gather data.\n",
        "    advantages = returns - values\n",
        "\n",
        "    # Convert tensors to a Tensorflow dataset\n",
        "    dataset = tf.data.Dataset.from_tensor_slices((states, actions, action_probs, advantages, returns))\n",
        "\n",
        "    # Shuffle the data set and set it up to be used for our target number of\n",
        "    # epochs for each step of PPO training.\n",
        "    dataset = dataset.shuffle(max_steps_per_episode * minibatch_size).repeat(num_epochs).batch(minibatch_size)\n",
        "\n",
        "    # Train over the gathered data for some number of iterations\n",
        "    loss, L_a, L_c, S = None, None, None, None\n",
        "    for batch in dataset:\n",
        "      mb_states = batch[0]\n",
        "      mb_actions = batch[1]\n",
        "      mb_action_probs = batch[2]\n",
        "      mb_advantages = batch[3]\n",
        "      mb_returns = batch[4]\n",
        "      mb_action_idx = tf.transpose(tf.stack([tf.range(mb_actions.shape[0]),\n",
        "          tf.squeeze(mb_actions, 1)]))\n",
        "      loss, L_a, L_c, S = train_minibatch(mb_states, mb_actions, mb_action_idx,\n",
        "          mb_action_probs, mb_advantages, mb_returns, model, optimizer,\n",
        "          critic_loss_fn, c1, c2, epsilon)\n",
        "\n",
        "    # Keep track of the loss for each training step\n",
        "    total_losses.append(loss)\n",
        "    actor_losses.append(L_a)\n",
        "    critic_losses.append(c1 * L_c)\n",
        "    entropy_terms.append(c2 * S)\n",
        "\n",
        "    # Update the progress bar for each PPO training step\n",
        "    steps.set_description(f'Finished step {step} with {gather_episodes} episode rollouts and {num_epochs} training epochs')\n",
        "    steps.set_postfix(episode_reward=episode_rewards[-gather_episodes:], running_reward=running_reward, max_running_reward=max_running_reward)\n",
        "\n",
        "    # Perform early stopping if our running reward is better than our threshold\n",
        "    if running_reward > reward_threshold:  \n",
        "        break\n",
        "\n",
        "# Plot the episodic reward over time. It should go up if we are doing things \n",
        "# properly!\n",
        "plt.plot(np.array(episode_rewards))\n",
        "plt.xlabel(\"Episode\")\n",
        "plt.ylabel(\"Episodic reward\")\n",
        "plt.show()\n",
        "\n",
        "# Track the total loss of the PPO function. This is useful to help tell if our\n",
        "# model is diverging due to an improper set of hyper-parameters.\n",
        "plt.plot(np.array(total_losses))\n",
        "plt.xlabel(\"PPO Step\")\n",
        "plt.ylabel(\"Total Loss\")\n",
        "plt.show()\n",
        "\n",
        "# Track the contribution of the actor loss component to the loss function. This\n",
        "# is only for debugging purposes.\n",
        "plt.plot(np.array(actor_losses))\n",
        "plt.xlabel(\"PPO Step\")\n",
        "plt.ylabel(\"Actor Loss\")\n",
        "plt.show()\n",
        "\n",
        "# Track the contribution of the critic loss component to the loss function. This\n",
        "# is only for debugging purposes.\n",
        "plt.plot(np.array(critic_losses))\n",
        "plt.xlabel(\"PPO Step\")\n",
        "plt.ylabel(\"Scaled Critic Loss\")\n",
        "plt.show()\n",
        "\n",
        "# Track the contribution of the entropy component to the loss function. This\n",
        "# is only for debugging purposes.\n",
        "plt.plot(np.array(entropy_terms))\n",
        "plt.xlabel(\"PPO Step\")\n",
        "plt.ylabel(\"Scaled Entropy\")\n",
        "plt.show()\n",
        "\n",
        "# Print out a final summary once training is done.\n",
        "if running_reward > reward_threshold:\n",
        "  print(f'\\nSolved at episode {step}: average reward: {running_reward:.2f}!')\n",
        "else:\n",
        "  print(f'\\nUnable to solve after {step} episodes. Average reward: {running_reward:.2f}')"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Finished step 834 with 4 episode rollouts and 4 training epochs:  67%|██████▋   | 834/1250 [20:38<10:17,  1.48s/it, episode_reward=[434.0, 436.0, 499.0, 499.0], max_running_reward=196, running_reward=195]\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "\n",
            "Solved at episode 834: average reward: 195.08!\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "r0-gRYrhCsVY"
      },
      "source": [
        "While we are setting a deterministic random seed, the training process does not always converge. This is possibly due to accumulated floating point errors or stochasticity of operations performed in the GPU.\n",
        "\n",
        "The following blocks allow us to visualize how our PPO-trained policy performs."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NYjefgs2eGpu"
      },
      "source": [
        "# Render an episode and save as a GIF file\n",
        "\n",
        "from IPython import display as ipythondisplay\n",
        "from PIL import Image\n",
        "from pyvirtualdisplay import Display\n",
        "\n",
        "\n",
        "display = Display(visible=0, size=(400, 300))\n",
        "display.start()\n",
        "\n",
        "\n",
        "def render_episode(env: gym.Env, model: tf.keras.Model, max_steps: int): \n",
        "  screen = env.render(mode='rgb_array')\n",
        "  im = Image.fromarray(screen)\n",
        "\n",
        "  images = [im]\n",
        "\n",
        "  state = env.reset()\n",
        "  for i in range(1, max_steps + 1):\n",
        "    action_probs, _ = model(tf.expand_dims(state, 0))\n",
        "    action = np.argmax(np.squeeze(action_probs))\n",
        "\n",
        "    state, _, done, _ = env.step(action)\n",
        "    state = tf.constant(state, dtype=tf.float32)\n",
        "\n",
        "    # Render screen every 10 steps\n",
        "    if i % 10 == 0:\n",
        "      screen = env.render(mode='rgb_array')\n",
        "      images.append(Image.fromarray(screen))\n",
        "\n",
        "    if done:\n",
        "      break\n",
        "\n",
        "  return images\n",
        "\n",
        "\n",
        "# Save GIF image\n",
        "images = render_episode(env, model, 5000)\n",
        "image_file = 'cartpole-v1.gif'\n",
        "# loop=0: loop forever, duration=1: play each frame for 1ms\n",
        "images[0].save(\n",
        "    image_file, save_all=True, append_images=images[1:], loop=0, duration=1)"
      ],
      "execution_count": 12,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qOLZuoSFeQjL",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 420
        },
        "outputId": "a50a4a3b-619a-4ff3-ef4b-e554768d71ba"
      },
      "source": [
        "import tensorflow_docs.vis.embed as embed\n",
        "embed.embed_file(image_file)"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<img 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\"/>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 13
        }
      ]
    }
  ]
}