Actor Critic Methods.ipynb

{
 "cells": [
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   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "# Actor Critic Methods"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "### Problems with Policy Gradient Methods and need for Actor-Critic Methods"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-02T00:31:10.468957Z",
     "start_time": "2021-07-02T00:31:10.449175Z"
    },
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "Policy Gradient methods have a major problem. We are in a situation of Monte Carlo, waiting until the end of episode to calculate the reward. We may conclude that if we have a high reward $R(t)$, all actions that we took were good, even if some of them were really bad.\n",
    "\n",
    "$\\text{good}\\qquad\\text{good}\\qquad\\quad\\text{bad}\\qquad\\qquad\\qquad\\quad\\text{good}$\n",
    "\n",
    "$A_1\\quad\\to\\quad A_2\\quad\\to\\quad A_3\\quad\\to\\quad\\cdots\\quad\\to\\quad A_n$\n",
    "\n",
    "\n",
    "As we can see in this example, even if $A_3$ was a bad action (led to negative rewards), all the actions will be averaged as good because the total reward was important.\n",
    "\n",
    "As a consequence, to have an optimal policy, we need a lot of samples. This produces slow learning, because it takes a lot of time to converge.\n",
    "\n",
    "What if, instead, we can do an update at each time step?\n",
    "\n",
    "The Actor Critic model is a better score function. Instead of waiting until the end of the episode as we do in **Monte Carlo REINFORCE**, we make an update at each step (**TD Learning**).\n",
    "\n",
    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)\n",
    "\n",
    "Because we do an update at each time step, we can't use the total rewards $R(t)$. Instead, we need to train a Critic model that approximates the value function (note that the value function calculates what is the _maximum expected future reward_ given a state and an action). This value function replaces the reward function in policy gradient that calculates the rewards only at the end of the episode.\n",
    "\n",
    "#### Introducing the Advantage function to stabilize learning\n",
    "\n",
    "As with the improvements in Deep Q Learning, **value-based methods have high variability**.\n",
    "\n",
    "To reduce this problem, the **advantage function** instead of the **value function** is used.\n",
    "\n",
    "The advantage function is defined as $A(s,a) = Q(s,a) - V(s)$\n",
    "\n",
    "This function will tell us the **improvement compared to the average action taken at any state**. In other words, this function calculates the extra reward we get if we take this action. The extra reward is what is beyond the expected value of that state.\n",
    "\n",
    "If $A(s,a) > 0$: the gradient is pushed in that direction.\n",
    "\n",
    "If $A(s,a) < 0$: the action $a$ does worse than the average value of that state and the gradient is pushed in the opposite direction.\n",
    "\n",
    "The problem of implementing this advantage function is that is requires two value functions — $Q(s,a)$ and $V(s)$. \n",
    "\n",
    "However, we can use the TD error as a good estimator of the advantage function.\n",
    "\n",
    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)\n",
    "\n",
    "**The insight of using advantage estimates rather than just discounted returns is to allow the agent to determine not just how good its actions were, but how much better they turned out to be than expected.** Intuitively, this allows the algorithm to focus on where the network's predictions were lacking.\n",
    "\n",
    "The full article can be found [here](https://www.freecodecamp.org/news/an-intro-to-advantage-actor-critic-methods-lets-play-sonic-the-hedgehog-86d6240171d/)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-01T22:42:18.949305Z",
     "start_time": "2021-07-01T22:42:18.942367Z"
    },
    "deletable": false,
    "editable": false
   },
   "outputs": [],
   "source": [
    "from IPython.lib.display import YouTubeVideo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "### Motivation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-01T22:42:20.665819Z",
     "start_time": "2021-07-01T22:42:20.495528Z"
    },
    "deletable": false,
    "editable": false
   },
   "outputs": [
    {
     "data": {
      "image/jpeg": 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AAAAAAAAAAAAAAAAAAAAAAAAD/9k=\n",
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"400\"\n",
       "            height=\"300\"\n",
       "            src=\"https://www.youtube.com/embed/dpFPlDtdxyQ\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x7fd8281cfa90>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "YouTubeVideo('dpFPlDtdxyQ')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "### Bias and Variance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-01T22:42:22.928820Z",
     "start_time": "2021-07-01T22:42:22.817975Z"
    },
    "deletable": false,
    "editable": false
   },
   "outputs": [
    {
     "data": {
      "image/jpeg": 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\n",
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"400\"\n",
       "            height=\"300\"\n",
       "            src=\"https://www.youtube.com/embed/_vnkkwm46uU\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x7fd82b625bd0>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "YouTubeVideo('_vnkkwm46uU')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "### Two Ways For Estimating Expected Returns: Bias-Variance Tradeoff in RL"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-07-01T22:42:24.960255Z",
     "start_time": "2021-07-01T22:42:24.820213Z"
    },
    "deletable": false,
    "editable": false
   },
   "outputs": [
    {
     "data": {
      "image/jpeg": 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       "\n",
       "        <iframe\n",
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       "            src=\"https://www.youtube.com/embed/2W6yIBDvfsQ\"\n",
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       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x7fd82816f8d0>"
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     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "YouTubeVideo('2W6yIBDvfsQ')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "### Not all Baselines are Critics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "deletable": false,
    "editable": false
   },
   "outputs": [],
   "source": [
    "YouTubeVideo('wqmqoiUuQHI')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   },
   "source": [
    "**Baselines computed using Monte-Carlo estimates are NOT critics (even if we use function approximators to estimate these baselines)**. However, in the literature, people do sometimes call them critics. The argument they often make as to why to call a neural network trained with Monte-Carlo estimates a `Critic` is because function approximators, such as a neural network, are biased as a byproduct that they are not perfect. That's a fair point, though, we prefer the distinction based on whether we pick a **Monte-Carlo** or a **TD estimate** to train our function approximator. *Now, definitely we should not be calling Actor-Critic methods every method that uses 2 neural networks*.\n",
    "\n",
    "Nevertheless, there are inconsistencies out there. We often see methods named `Actor-Critic` when they are not.\n",
    "\n",
    "For example, according to Sutton's RL book (page 333)\n",
    "\n",
    "> Although the **REINFORCE-with-baseline** method learns both a policy and a state-value function, we do not consider it to be an actor–critic method because its state-value function is used only as a baseline, not as a critic. That is, it is not used for bootstrapping (updating the value estimate for a state from the estimated values of subsequent states), but only as a baseline for the state whose estimate is being updated."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "### Policy-based, Value-based and Actor-Critic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "deletable": false,
    "editable": false
   },
   "outputs": [],
   "source": [
    "YouTubeVideo('iyin896PNEc')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "### A Basic Actor-Critic Agent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "deletable": false,
    "editable": false
   },
   "outputs": [],
   "source": [
    "YouTubeVideo('KdHQ24hBKho')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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    "run_control": {
     "frozen": true
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   },
   "source": [
    "In the previous video $V(s;\\theta_v)\\text{ or }V_\\pi(s;\\theta_v)$ and $A(s,a)\\text{ or }A_\\pi(s,a)$ are the evaluations of the value and advantage functions respectively w.r.t. to a given policy $\\pi$.\n",
    "\n",
    "The other thing to note is the use of $\\theta_v$ in some value (or advantage) functions and not in others. This only means that such value function is using a neural network parameterized by $\\theta_v$. For example, $V(s;\\theta_v)$ is using a neural network as a function approximator, but $A(s,a)$ is not. We are calculating the advantage function $A(s,a)$ using the state-value function $V(s;\\theta_v)$, but $A(s,a)$ is not using function approximation directly."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "In actor-critic the critic (value function) gets updated based on the difference of the immediate reward $R_1$ and what the critic expected: $V(S_2) - V(S_1)$, and then the actor (policy) only looks at the critic while learning. The reward used in the policy gradient to update the actor is $V(S_2) - V(S_1)$, it doesn't see specific $R_i$ values. This value difference is often much less noisy than $R_1$, it might also be a bit wrong."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "### A3C: Asynchronous Advantage Actor-Critic\n",
    "\n",
    "#### N-step Bootstrapping"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "deletable": false,
    "editable": false
   },
   "outputs": [],
   "source": [
    "YouTubeVideo('twNXFplIAP8')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "Bootstrapping or Temporal Difference roughly means that we estimate the value of the action as a sum of our immediate reward plus an approximation (using a value function) of future rewards we expect from our next state. So if we play a game $S_1,A_1,R_1,S_2,A_2,\\cdots$ then our first action gets reward $R_1 + V(S_2)$ and not $R_1+R_2+R_3+\\cdots$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "#### Parallel Training"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "deletable": false,
    "editable": false
   },
   "outputs": [],
   "source": [
    "YouTubeVideo('kKRbAKhjACo')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "#### Off-policy vs. On-policy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "deletable": false,
    "editable": false
   },
   "outputs": [],
   "source": [
    "YouTubeVideo('AZiy5R0DESU')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "[Link](https://arxiv.org/abs/1611.02247) to the Q-Prop paper."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "### A2C: Advantage Actor-Critic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "deletable": false,
    "editable": false
   },
   "outputs": [],
   "source": [
    "YouTubeVideo('fIWe3xA97DA')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "### GAE: Generalized Advantage Estimation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "deletable": false,
    "editable": false
   },
   "outputs": [],
   "source": [
    "YouTubeVideo('oLFocWp0dt0')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "[Link](https://arxiv.org/abs/1506.02438) to the GAE paper."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "## Learning to play Boxing using Advantage Actor Critic (A2C)\n",
    "\n",
    "We will implement and train a policy to play [atari-boxing](https://www.endtoend.ai/envs/gym/atari/#variants), using only the pixels as input. We will use convolutional neural nets and multiprocessing to implement and train our policy.\n",
    "\n",
    "Watch the [A2C video](https://www.youtube.com/watch?v=LiUBJje2N0c) for a detailed code walk-through."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "### Import the Necessary Packages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "deletable": false,
    "editable": false
   },
   "outputs": [],
   "source": [
    "import time\n",
    "import copy\n",
    "import os.path\n",
    "import numpy as np\n",
    "import random as rand\n",
    "from collections import deque, namedtuple\n",
    "\n",
    "import gym\n",
    "gym.logger.set_level(40)                              # suppress warnings (please remove if gives error)\n",
    "\n",
    "from utils.ParallelEnvironments import ParallelEnv \n",
    "\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import animation\n",
    "%matplotlib inline\n",
    "\n",
    "import torch\n",
    "import torch.nn as nn\n",
    "import torch.optim as optim\n",
    "import torch.nn.functional as F\n",
    "\n",
    "from IPython.display import display as Display\n",
    "from IPython.display import HTML\n",
    "from pyvirtualdisplay import Display as display\n",
    "display = display(visible=0, size=(1400, 900))\n",
    "display.start()\n",
    "is_ipython = 'inline' in plt.get_backend()\n",
    "if is_ipython:\n",
    "    from IPython import display\n",
    "plt.ion()\n",
    "\n",
    "\n",
    "device = torch.device('cuda:0' if torch.cuda.is_available() else 'cpu')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "`BoxingDeterministic` does not contain random frameskip, so it's faster to train than the vanilla `Boxing-v4` environment. More on the different variants of atari enviroments can be found [here](https://www.endtoend.ai/envs/gym/atari/#variants)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ENVIRONMENT = 'BoxingDeterministic-v4'\n",
    "NOOP        = 0\n",
    "FIRE        = 1\n",
    "UP          = 2\n",
    "RIGHT       = 3\n",
    "LEFT        = 4\n",
    "DOWN        = 5\n",
    "UPRIGHT     = 6\n",
    "UPLEFT      = 7\n",
    "DOWNRIGHT   = 8\n",
    "DOWNLEFT    = 9\n",
    "ACTIONS     = [NOOP, FIRE, UP, RIGHT, LEFT, DOWN, UPRIGHT, UPLEFT, DOWNRIGHT, DOWNLEFT]\n",
    "\n",
    "A2C_MODEL_FILE = './models/a2c-boxing.pt'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "RANDOM_SEED = 12345"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "deletable": false,
    "editable": false
   },
   "outputs": [],
   "source": [
    "env = gym.make(ENVIRONMENT)\n",
    "\n",
    "env.seed(RANDOM_SEED)\n",
    "rand.seed(RANDOM_SEED)\n",
    "torch.manual_seed(RANDOM_SEED)\n",
    "\n",
    "print('List of available actions: ', env.unwrapped.get_action_meanings())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "We will only use these actions:\n",
    "```\n",
    "NOOP        = 0\n",
    "FIRE        = 1\n",
    "UP          = 2\n",
    "RIGHT       = 3\n",
    "LEFT        = 4\n",
    "DOWN        = 5\n",
    "UPRIGHT     = 6\n",
    "UPLEFT      = 7\n",
    "DOWNRIGHT   = 8\n",
    "DOWNLEFT    = 9\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "### Preprocessing\n",
    "\n",
    "To speed up training, we can simplify the input by cropping the images and use every other pixel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "code_folding": [
     0,
     9
    ],
    "deletable": false,
    "editable": false
   },
   "outputs": [],
   "source": [
    "def preprocess_single(image, bkg_color = np.array([110, 156, 66])):\n",
    "    '''\n",
    "    preprocess a single frame (210x160x3)\n",
    "    crop image and downsample to 74x74\n",
    "    stack two frames together as input\n",
    "    '''\n",
    "    image = np.mean(image[32:-30:2,6:-6:2] - bkg_color, axis=-1) / 255.0\n",
    "    return image\n",
    "\n",
    "def preprocess_batch(images, bkg_color = np.array([110, 156, 66])):\n",
    "    '''\n",
    "    convert outputs of parallelEnv to inputs of pytorch neural net\n",
    "    this is useful for batch processing especially on the GPU\n",
    "    '''\n",
    "    list_of_images = np.asarray(images)\n",
    "    if len(list_of_images.shape) < 5:\n",
    "        list_of_images = np.expand_dims(list_of_images, 1)\n",
    "    # subtract background and crop\n",
    "    list_of_images_prepro = np.mean(list_of_images[:,:,32:-30:2,6:-6:2] - bkg_color, axis=-1) / 255.0\n",
    "    batch_input = np.swapaxes(list_of_images_prepro, 0, 1)\n",
    "    # torch.Size([N, len(images), 74, 74]) i.e. (#data_points, #frames, 74, 74)\n",
    "    return torch.from_numpy(batch_input).float().to(device)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "#### This is what a preprocessed image looks like"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "code_folding": [
     2
    ],
    "deletable": false,
    "editable": false
   },
   "outputs": [],
   "source": [
    "env.reset()\n",
    "env.step(0)\n",
    "for _ in range(20): # get a frame after 20 steps\n",
    "    frame, _, _, _ = env.step(1)\n",
    "\n",
    "plt.subplot(1,2,1)\n",
    "plt.imshow(frame)\n",
    "plt.title('original image')\n",
    "\n",
    "plt.subplot(1,2,2)\n",
    "plt.title('preprocessed image')\n",
    "\n",
    "# 74x74 black and white image\n",
    "plt.imshow(preprocess_single(frame), cmap='Greys')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "### Policy\n",
    " \n",
    "Now, we define our **`Actor Critic`** network. The input is the stack of four different frames (which captures the movement), and the output is a number $\\Pr(a|s)$ i.e. the probability of choosing one of the $10$ actions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "code_folding": [
     0
    ],
    "deletable": false,
    "editable": false
   },
   "outputs": [],
   "source": [
    "class ActorCriticNetwork(nn.Module):\n",
    "    '''\n",
    "    set up an actor critic network\n",
    "    \n",
    "    Params\n",
    "    ======\n",
    "        input: Nx4x74x74 shaped vector i.e. N data/input, 4 frames/channels, each image is 74x74\n",
    "        outout: Nx10 shaped vector representing the probabilities of chosing one of the 10 actions\n",
    "                Nx1  shaped vector representing the value function estimate of the input state\n",
    "    '''\n",
    "    def __init__(self):\n",
    "        super(ActorCriticNetwork, self).__init__()\n",
    "        # in_channel = number of channels in the input image\n",
    "        # out_channel = number of channels in the output feature map = number of filters\n",
    "        # outputsize = (inputsize - kernel_size + stride) / stride  (round up if not an integer)\n",
    "        # 4x74x74 to 8x35x35\n",
    "        self.conv1 = nn.Conv2d(4, 8, kernel_size=6, stride=2, bias=False)\n",
    "        # 8x35x35 to 16x11x11\n",
    "        self.conv2 = nn.Conv2d(8, 16, kernel_size=5, stride=3)\n",
    "        self.fc = nn.Linear(16*11*11, 512)\n",
    "\n",
    "        self.actor = nn.Linear(512, 10) # 10 actions\n",
    "        self.critic = nn.Linear(512, 1) # 1 value function estimate\n",
    "\n",
    "    def forward(self, x):\n",
    "        # shape of x is Nx4x74x74 i.e. N data/input, 4 frames/channels, each image is 74x74\n",
    "        x = x.to(device)\n",
    "        x = F.relu(self.conv1(x))\n",
    "        x = F.relu(self.conv2(x))\n",
    "        x = x.view(x.size(0), -1) # flatten the tensor\n",
    "        x = F.relu(self.fc(x))\n",
    "\n",
    "        logits = self.actor(x)\n",
    "        v = self.critic(x)\n",
    "\n",
    "        ####### choice 1 (pytorch native) #######\n",
    "        distribution = torch.distributions.Categorical(logits=logits)\n",
    "        action = distribution.sample()\n",
    "        log_prob = distribution.log_prob(action).unsqueeze(-1)\n",
    "        entropy = distribution.entropy().unsqueeze(-1)\n",
    "        #########################################\n",
    "        \n",
    "        ###### choice 2 (custom equivalent) #####\n",
    "#         logits = logits - torch.log(torch.exp(logits).sum())\n",
    "#         distribution = F.softmax(logits, dim=-1)\n",
    "#         samples = torch.rand(distribution.shape[0], requires_grad=False).unsqueeze(-1).cpu()\n",
    "#         cdf = torch.cumsum(distribution.detach(), dim=1).cpu()\n",
    "#         action = torch.argmax(cdf >= samples, dim=1).to(device)\n",
    "#         log_prob = torch.log(distribution.gather(1, action.unsqueeze(-1)))\n",
    "#         entropy = - (distribution * torch.log(distribution)).sum(dim=1).unsqueeze(-1)\n",
    "        ########################################\n",
    "        \n",
    "        return {\n",
    "            'action': action,\n",
    "            'log_pi_a': log_prob.double(),\n",
    "            'entropy': entropy.double(),\n",
    "            'v': v.double()\n",
    "        }"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "#### Drawing Samples from a Distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "deletable": false,
    "editable": false
   },
   "outputs": [],
   "source": [
    "YouTubeVideo('nNK4xKkAapM', start=1135)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "### Game visualization\n",
    "\n",
    "Here we define a function that plays a game and shows learning progress."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "code_folding": [
     0,
     14
    ],
    "deletable": false,
    "editable": false
   },
   "outputs": [],
   "source": [
    "def animate_frames(frames):\n",
    "    'function to animate a list of frames'\n",
    "    \n",
    "    def display_animation(anim):\n",
    "        plt.close(anim._fig)\n",
    "        return HTML(anim.to_jshtml())\n",
    "\n",
    "    plt.axis('off')\n",
    "    cmap = None if len(frames[0].shape) == 3 else 'Greys' # color option for plotting, use Greys for greyscale\n",
    "    patch = plt.imshow(frames[0], cmap=cmap)  \n",
    "    fanim = animation.FuncAnimation(plt.gcf(), lambda x: patch.set_data(frames[x]), frames = len(frames), interval=30)\n",
    "    Display(display_animation(fanim))\n",
    "\n",
    "\n",
    "def play(env, policy, time=2000, preprocess=None, nrand=5):\n",
    "    '''\n",
    "    play a game and display the animation\n",
    "    \n",
    "    Params\n",
    "    ======\n",
    "        nrand (int): number of random steps before using the policy\n",
    "        preprocess (func): add the argument preprocess_single to see what the agent sees\n",
    "    '''\n",
    "    env.reset()\n",
    "    env.step(0) # start game\n",
    "    \n",
    "    # perform nrand random steps in the beginning\n",
    "    for _ in range(nrand):\n",
    "        frame1, _, _, _ = env.step(np.random.choice(ACTIONS))\n",
    "        frame2, _, _, _ = env.step(0)\n",
    "        frame3, _, _, _ = env.step(np.random.choice(ACTIONS))\n",
    "        frame4, _, _, _ = env.step(0)\n",
    "    \n",
    "    anim_frames = []\n",
    "    \n",
    "    for i in range(time):\n",
    "        frame_input = preprocess_batch([frame1, frame2, frame3, frame4])\n",
    "        prediction = policy(frame_input)\n",
    "\n",
    "        action = prediction['action'].item()\n",
    "        frame1, _, is_done, _ = env.step(action)\n",
    "        frame2, _, is_done, _ = env.step(0)\n",
    "        frame3, _, is_done, _ = env.step(action)\n",
    "        frame4, _, is_done, _ = env.step(0)\n",
    "        frames = [frame1, frame2, frame3, frame4]\n",
    "        \n",
    "        anim_frames.extend(list(map(preprocess, frames)) if preprocess else frames)\n",
    "        \n",
    "        if is_done:\n",
    "            break\n",
    "    animate_frames(anim_frames)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "The `white` agent is supposed to be controlled by the RL algorithm and the `black` agent is controlled by the environment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "deletable": false,
    "editable": false
   },
   "outputs": [],
   "source": [
    "policy = ActorCriticNetwork().to(device)\n",
    "\n",
    "play(env, policy, time=400) # add the argument \"preprocess=preprocess_single\" to see what the agent sees"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "### Rolled Out Experience Replay Buffer\n",
    "\n",
    "During training, we need to collect samples. To make things efficient we use parallelized environments to collect multiple trajectories at once."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "code_folding": [
     0
    ],
    "deletable": false,
    "editable": false
   },
   "outputs": [],
   "source": [
    "class Storage:\n",
    "    def __init__(self, memory_size, keys=None):\n",
    "        if keys is None: keys = []\n",
    "        keys = keys + ['state', 'action', 'reward', 'mask', 'v', 'q', 'q_a', 'pi', 'ret',\n",
    "                       'entropy', 'advantage', 'log_pi', 'log_pi_a', 'mean', 'next_state']\n",
    "        self.keys = keys\n",
    "        self.memory_size = memory_size\n",
    "        self.reset()\n",
    "\n",
    "    def feed(self, data):\n",
    "        for k, v in data.items():\n",
    "            if k not in self.keys:\n",
    "                raise RuntimeError('Undefined key')\n",
    "            getattr(self, k).append(v)\n",
    "\n",
    "    def placeholder(self):\n",
    "        for k in self.keys:\n",
    "            v = getattr(self, k)\n",
    "            if len(v) == 0:\n",
    "                setattr(self, k, [None] * self.memory_size)\n",
    "\n",
    "    def reset(self):\n",
    "        for key in self.keys:\n",
    "            setattr(self, key, [])\n",
    "        self.pos = 0\n",
    "        self._size = 0\n",
    "\n",
    "    def extract(self, keys):\n",
    "        data = [getattr(self, k)[:self.memory_size] for k in keys]\n",
    "        data = map(lambda x: torch.cat(x, dim=0), data)\n",
    "        Entry = namedtuple('Entry', keys)\n",
    "        return Entry(*list(data))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "### Actor-Critic Objective Function for Training\n",
    "\n",
    "```\n",
    "N (number of parallel agents) = 4\n",
    "T (rollout length)  = 5\n",
    "```\n",
    "\n",
    "We have two choices:\n",
    "  1. $\\nabla_\\theta U(\\theta)=\\frac{1}{N}{\\displaystyle\\sum^N_{i=1}}{\\displaystyle\\sum^T_{t=1}} A\\left(s_t^{(i)},a_t^{(i)}\\right)\\cdot\\nabla_\\theta\\log\\left(\\pi_\\theta\\left(a^{(i)}_t|s^{(i)}_t\\right)\\right)\\quad+\\quad\\frac{1}{N}{\\displaystyle\\sum^N_{i=1}}\\frac{1}{T}{\\displaystyle\\sum^T_{t=1}}\\mathcal{E}_t^{(i)}\\quad-\\quad\\frac{1}{N}{\\displaystyle\\sum^N_{i=1}}\\frac{1}{T}{\\displaystyle\\sum^T_{t=1}}\\frac{1}{2}\\left[A\\left(s_t^{(i)}, a_t^{(i)}\\right)\\right]^2$\n",
    "  2. $\\nabla_\\theta U(\\theta)=\\frac{1}{N}{\\displaystyle\\sum^N_{i=1}}\\frac{1}{T}{\\displaystyle\\sum^T_{t=1}} A\\left(s_t^{(i)}, a_t^{(i)}\\right)\\cdot\\nabla_\\theta\\log\\left(\\pi_\\theta\\left(a^{(i)}_t|s^{(i)}_t\\right)\\right)\\quad+\\quad\\frac{1}{N}{\\displaystyle\\sum^N_{i=1}}\\frac{1}{T}{\\displaystyle\\sum^T_{t=1}}\\mathcal{E}_t^{(i)}\\quad-\\quad\\frac{1}{N}{\\displaystyle\\sum^N_{i=1}}\\frac{1}{T}{\\displaystyle\\sum^T_{t=1}}\\frac{1}{2}\\left[A\\left(s_t^{(i)}, a_t^{(i)}\\right)\\right]^2$\n",
    "\n",
    "Advantage function *estimate*, $\\quad A\\left(s_t^{(i)}, a_t^{(i)}\\right)={\\displaystyle\\sum^{T-t}_{j=0}}\\gamma^j r_{t+j}^{(i)}+\\gamma^{T-t+1}V_{\\theta_v}\\left(s_{T+1}\\right)-V_{\\theta_v}\\left(s_t\\right)\\quad$ where $V_{\\theta_v}$ is the value function *estimate*.\n",
    "\n",
    "Entropy, $\\quad\\mathcal{E}_t^{(i)}=-{\\displaystyle\\sum_{a\\in\\mathcal{A}}}\\pi_\\theta\\left(a|s^{(i)}_t\\right)\\cdot\\log\\left(\\pi_\\theta\\left(a|s^{(i)}_t\\right)\\right)$\n",
    "\n",
    "In equation 2, usually it's useful to divide by the rollout length since the rollout length of each trajectory is fixed and this division will keep the gradient estimate small lest we may overshoot the local maximum. Equation 2 was used by the original author.\n",
    "\n",
    "$\\theta_{new}\\leftarrow\\theta_{old}+\\alpha\\cdot\\nabla_\\theta U(\\theta)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "### Training\n",
    "\n",
    "We are now ready to train our policy!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "### Hyperparameters for Training"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "USE_GAE           = False\n",
    "LAMBDA            = 1.0\n",
    "GAMMA             = 0.99\n",
    "LEARNING_RATE     = 1e-4\n",
    "ENTROPY_WEIGHT    = 0.01\n",
    "VALUE_LOSS_WEIGHT = 1.0\n",
    "N_WORKERS         = 4\n",
    "ROLLOUT_LENGTH    = 5\n",
    "GRADIENT_CLIP     = 5\n",
    "MAX_STEPS         = 250000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "code_folding": [
     0,
     5
    ],
    "deletable": false,
    "editable": false
   },
   "outputs": [],
   "source": [
    "class SignNormalizer():\n",
    "    'To normalize the rewards'\n",
    "    def __call__(self, x):\n",
    "        return np.sign(x)\n",
    "\n",
    "class A2CAgent():\n",
    "    def __init__(self, n_step_skip=5, log_interval=50, save_interval=100, eval_interval=5):\n",
    "        '''\n",
    "        params\n",
    "        ======\n",
    "            n_step_skip(int)  : skip this many random steps\n",
    "            log_interval(int) : log progress after every this many steps\n",
    "            save_interval(int): save the model after every this many steps\n",
    "            eval_interval(int): evaluate the model after every this many steps\n",
    "        '''\n",
    "        self.use_gae = USE_GAE\n",
    "        self.λ = LAMBDA\n",
    "        \n",
    "        self.γ = GAMMA\n",
    "        self.entropy_weight = ENTROPY_WEIGHT\n",
    "        self.value_loss_weight = VALUE_LOSS_WEIGHT\n",
    "        \n",
    "        self.n_workers = N_WORKERS\n",
    "        self.rollout_length = ROLLOUT_LENGTH\n",
    "        self.gradient_clip = GRADIENT_CLIP\n",
    "        self.max_steps = MAX_STEPS\n",
    "\n",
    "        self.envs = ParallelEnv(ENVIRONMENT, self.n_workers, seed=RANDOM_SEED)\n",
    "        self.network = ActorCriticNetwork().to(device)\n",
    "        self.optimizer = torch.optim.RMSprop(self.network.parameters(), lr=LEARNING_RATE, alpha=0.99, eps=1e-5)\n",
    "        \n",
    "        self.total_steps = 0\n",
    "        self.log_interval = log_interval\n",
    "        self.save_interval = save_interval\n",
    "        self.eval_interval = eval_interval\n",
    "        \n",
    "        if os.path.isfile(A2C_MODEL_FILE):\n",
    "            # load training checkpoints from file\n",
    "            map_location = (lambda storage, loc: storage.cuda()) if torch.cuda.is_available() else 'cpu'\n",
    "            checkpoint = torch.load(A2C_MODEL_FILE, map_location=map_location)\n",
    "            self.network.load_state_dict(checkpoint['model_state_dict'])\n",
    "            self.optimizer.load_state_dict(checkpoint['optimizer_state_dict'])\n",
    "            self.start_step = checkpoint['start_step']\n",
    "            self.eval_reward = checkpoint['eval_reward']\n",
    "        else:\n",
    "            # start training from scratch\n",
    "            self.start_step = 0\n",
    "            self.eval_reward = np.array([])\n",
    "\n",
    "        self.network.train()\n",
    "        self.envs.reset()\n",
    "\n",
    "        # skip 'n_step_skip' random steps\n",
    "        for _ in range(n_step_skip):\n",
    "            frames1, rewards1, _, _ = self.envs.step(np.random.choice(ACTIONS, self.n_workers))\n",
    "            frames2, rewards2, _, _ = self.envs.step(np.random.choice(ACTIONS, self.n_workers))\n",
    "            frames3, rewards3, _, _ = self.envs.step(np.random.choice(ACTIONS, self.n_workers))\n",
    "            frames4, rewards4, _, _ = self.envs.step(np.random.choice(ACTIONS, self.n_workers))\n",
    "\n",
    "        # preprocess_batch properly converts four frames from all workers into shape (N, 4, 74, 74),\n",
    "        # the proper input for the policy that is required when building CNN with pytorch\n",
    "        # N = self.n_workers\n",
    "        self.states = preprocess_batch([frames1, frames2, frames3, frames4])\n",
    "        \n",
    "    def step(self):\n",
    "        storage = Storage(self.rollout_length)\n",
    "        states = self.states\n",
    "        for _ in range(self.rollout_length):\n",
    "            prediction = self.network(states)\n",
    "            frames1, rewards1, terminals1, _ = self.envs.step([NOOP] * self.n_workers)\n",
    "            frames2, rewards2, terminals2, _ = self.envs.step(prediction['action'].cpu().detach().numpy())\n",
    "            frames3, rewards3, terminals3, _ = self.envs.step([NOOP] * self.n_workers)\n",
    "            frames4, rewards4, terminals4, _ = self.envs.step(prediction['action'].cpu().detach().numpy())\n",
    "            states = preprocess_batch([frames1, frames2, frames3, frames4])   \n",
    "\n",
    "            rewards = rewards1 + rewards2 + rewards3 + rewards4\n",
    "            # rewards = SignNormalizer(rewards)\n",
    "\n",
    "            terminals = np.stack([terminals1, terminals2, terminals3, terminals4], axis=1).any(axis=1)\n",
    "            for index, is_done in enumerate(terminals):\n",
    "                if is_done:\n",
    "                    self.envs.reset_individual(index)\n",
    "\n",
    "            storage.feed(prediction)\n",
    "            storage.feed({\n",
    "                'reward': torch.tensor(rewards).to(device).unsqueeze(-1),\n",
    "                'mask': torch.tensor(1 - terminals, dtype=torch.double).to(device).unsqueeze(-1)\n",
    "            })\n",
    "\n",
    "        self.total_steps += 1\n",
    "        self.states = states\n",
    "        prediction = self.network(states)\n",
    "        storage.feed(prediction)\n",
    "        storage.placeholder()\n",
    "\n",
    "        advantages = torch.tensor(np.zeros((self.n_workers, 1)))\n",
    "        returns = prediction['v'].detach()\n",
    "        for i in reversed(range(self.rollout_length)):    \n",
    "            returns = storage.reward[i] + self.γ * storage.mask[i] * returns\n",
    "            if not self.use_gae:\n",
    "                advantages = returns - storage.v[i].detach()\n",
    "            else:\n",
    "                td_error = storage.reward[i] + self.γ * storage.mask[i] * storage.v[i + 1] - storage.v[i]\n",
    "                advantages = advantages * self.λ * self.discount * storage.mask[i] + td_error\n",
    "            storage.advantage[i] = advantages.detach()\n",
    "            storage.ret[i] = returns.detach()\n",
    "\n",
    "        entries = storage.extract(['log_pi_a', 'v', 'ret', 'advantage', 'entropy'])\n",
    "\n",
    "        # actor objective function        \n",
    "        policy_gradient_equation_1 = (entries.log_pi_a.view(-1, self.n_workers) * entries.advantage.view(-1, self.n_workers)).sum(dim=0).mean()\n",
    "        policy_gradient_equation_2 = (entries.log_pi_a * entries.advantage).mean()\n",
    "        policy_gradient = policy_gradient_equation_2\n",
    "\n",
    "        # critic loss\n",
    "        value_gradient = 0.5 * (entries.ret - entries.v).pow(2).mean()\n",
    "\n",
    "        entropy_regularization = entries.entropy.mean()\n",
    "\n",
    "        self.optimizer.zero_grad()\n",
    "        loss = - policy_gradient - self.entropy_weight * entropy_regularization + self.value_loss_weight * value_gradient\n",
    "        loss.backward()\n",
    "        nn.utils.clip_grad_norm_(self.network.parameters(), self.gradient_clip)\n",
    "        self.optimizer.step()\n",
    "\n",
    "        # evaluate the model\n",
    "        if self.total_steps % self.eval_interval == 0:\n",
    "            self.eval_reward = np.append(self.eval_reward, self.eval_episode())\n",
    "\n",
    "        # display progress\n",
    "        print('\\r' + ' ' * 120, end='')\n",
    "        print('\\rIteration: {}/{}    Avg. Episodic Score: {:.4f}    Recent Episodic Scores: {}'.format(\n",
    "            self.start_step + self.total_steps,\n",
    "            self.start_step + self.max_steps,\n",
    "            self.eval_reward[-100:].mean() if len(self.eval_reward[-100:]) else 0.0,\n",
    "            self.eval_reward[-5:]\n",
    "        ), end='')\n",
    "        if self.total_steps % self.log_interval == 0:\n",
    "            print('\\r' + ' ' * 120, end='')\n",
    "            print('\\rIteration: {}/{}    Avg. Episodic Score: {:.4f}'.format(\n",
    "                self.start_step + self.total_steps,\n",
    "                self.start_step + self.max_steps,\n",
    "                self.eval_reward[-100:].mean()\n",
    "            ))   \n",
    "\n",
    "        # save the model\n",
    "        if self.total_steps % self.save_interval == 0:\n",
    "            torch.save({\n",
    "                'start_step': self.start_step + self.total_steps,\n",
    "                'model_state_dict': self.network.state_dict(),\n",
    "                'optimizer_state_dict': self.optimizer.state_dict(),\n",
    "                'eval_reward': self.eval_reward\n",
    "            }, A2C_MODEL_FILE)\n",
    "\n",
    "    def close(self):\n",
    "        self.envs.close()\n",
    "        \n",
    "    def eval_episode(self):\n",
    "        env = gym.make(ENVIRONMENT)\n",
    "        env.reset()\n",
    "        frame1, reward1, _, _ = env.step(np.random.choice(ACTIONS))\n",
    "        frame2, reward2, _, _ = env.step(np.random.choice(ACTIONS))\n",
    "        frame3, reward3, _, _ = env.step(np.random.choice(ACTIONS))\n",
    "        frame4, reward4, _, _ = env.step(np.random.choice(ACTIONS))        \n",
    "        state = preprocess_batch([frame1, frame2, frame3, frame4])\n",
    "        reward = 0\n",
    "        while True:\n",
    "            prediction = self.network(state)\n",
    "            frame1, reward1, terminal1, _ = env.step(NOOP)\n",
    "            frame2, reward2, terminal2, _ = env.step(prediction['action'].item())\n",
    "            frame3, reward3, terminal3, _ = env.step(NOOP)\n",
    "            frame4, reward4, terminal4, _ = env.step(prediction['action'].item())\n",
    "            state = preprocess_batch([frame1, frame2, frame3, frame4])\n",
    "            reward += reward1 + reward2 + reward3 + reward4\n",
    "            if terminal1 or terminal2 or terminal3 or terminal4:\n",
    "                break\n",
    "        env.close()\n",
    "        return reward"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "#### Training Loop"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "deletable": false,
    "editable": false
   },
   "outputs": [],
   "source": [
    "agent = A2CAgent()\n",
    "\n",
    "while agent.total_steps < agent.max_steps:\n",
    "    try:\n",
    "        agent.step()\n",
    "    except KeyboardInterrupt:\n",
    "        print('\\nTraining Interrupted')\n",
    "        break\n",
    "agent.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "### Plot Episodic Scores over Time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "deletable": false,
    "editable": false
   },
   "outputs": [],
   "source": [
    "plt.plot(agent.eval_reward);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "### Play Game after Training"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "LOAD_MODEL_FILE = A2C_MODEL_FILE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "deletable": false,
    "editable": false
   },
   "outputs": [],
   "source": [
    "env = gym.make(ENVIRONMENT)\n",
    "env.seed(int(time.time()))\n",
    "policy = ActorCriticNetwork().to(device)\n",
    "\n",
    "# load the weights from file\n",
    "map_location = (lambda storage, loc: storage.cuda()) if torch.cuda.is_available() else 'cpu'\n",
    "policy.load_state_dict(torch.load(LOAD_MODEL_FILE, map_location=map_location)['model_state_dict'])\n",
    "\n",
    "policy.eval()\n",
    "\n",
    "play(env, policy)\n",
    "\n",
    "env.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "| Pytorch Sampling    |  Custom Sampling    |\n",
    "|:------------------: | :-----------------: |\n",
    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) 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) |"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "## DDPG: Deep Deterministic Policy Gradient\n",
    "\n",
    "### Continuous Action Space"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "deletable": false,
    "editable": false
   },
   "outputs": [],
   "source": [
    "YouTubeVideo('0NVOPIyrr98')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "In the [DDPG paper](https://arxiv.org/abs/1509.02971), they introduced this algorithm as an `Actor-Critic` method. But, some researchers think DDPG is best classified as a DQN method for continuous action spaces (along with [NAF](https://arxiv.org/abs/1603.00748))."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "#### Soft Updates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "deletable": false,
    "editable": false
   },
   "outputs": [],
   "source": [
    "YouTubeVideo('RT-HDnAVe9o')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "deletable": false,
    "editable": false
   },
   "outputs": [],
   "source": [
    "YouTubeVideo('rRuiMhijw_s', start=70)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "![DDPG 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)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "## Application of Deep Deterministic Policy Gradients (DDPG)\n",
    "\n",
    "We'll implement a DDPG agent with OpenAI Gym's [BipedalWalker](https://gym.openai.com/envs/BipedalWalker-v2/) and [Pendulum](https://gym.openai.com/envs/Pendulum-v0/) environment.\n",
    "\n",
    "Watch the [DDPG video](https://www.youtube.com/watch?v=08V9r3NgFSE) for a detailed code walk-through."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "### Instantiate the Environment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ENVIRONMENT = 'Pendulum-v0'\n",
    "ENVIRONMENT = 'BipedalWalker-v3'\n",
    "\n",
    "DDPG_MODEL_FILE = './models/ddpg.pt'\n",
    "\n",
    "RANDOM_SEED = 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "deletable": false,
    "editable": false
   },
   "outputs": [],
   "source": [
    "env = gym.make(ENVIRONMENT)\n",
    "\n",
    "ACTION_SIZE = env.action_space.shape[0]\n",
    "STATE_SIZE  = env.observation_space.shape[0]\n",
    "\n",
    "env.close()\n",
    "\n",
    "torch.manual_seed(RANDOM_SEED)\n",
    "rand.seed(RANDOM_SEED)\n",
    "env.seed(RANDOM_SEED)\n",
    "\n",
    "print('State Space: ', env.observation_space)\n",
    "print('Action Space: ', env.action_space)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "### The Actor-Critic Network\n",
    "\n",
    "If training is too slow, increasing the **Learning Rate** by a factor of 2-3 and/or adding **BatchNorm/LayerNorm** layers often helps.\n",
    "\n",
    "```python\n",
    "class Model(nn.Module):\n",
    "    def __init__(self, input_units, output_units, hidden_units=128):\n",
    "        super(Model, self).__init__()\n",
    "        self.fc1 = nn.Linear(input_units, hidden_units)\n",
    "        self.fc2 = nn.Linear(hidden_units, output_units)\n",
    "        self.bn = nn.BatchNorm1d(hidden_units)\n",
    "        # self.ln = nn.LayerNorm(hidden_units)\n",
    "    def forward(self, x):\n",
    "        x = F.relu(self.fc1(x))\n",
    "        x = self.bn(x)\n",
    "        # x = self.ln(x)\n",
    "        return F.tanh(self.fc2(x))\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "code_folding": [
     0,
     6,
     40
    ],
    "deletable": false,
    "editable": false
   },
   "outputs": [],
   "source": [
    "def hidden_init(layer):\n",
    "    fan_in = layer.weight.data.size()[0]\n",
    "    lim = 1.0 / np.sqrt(fan_in)\n",
    "    return -lim, lim\n",
    "\n",
    "\n",
    "class Actor(nn.Module):\n",
    "    '''Actor (Policy) Model'''\n",
    "\n",
    "    def __init__(self, state_size, action_size, fc1_units=128, fc2_units=256):\n",
    "        '''Initialize parameters and build model.\n",
    "        Params\n",
    "        ======\n",
    "            state_size (int): Dimension of each state\n",
    "            action_size (int): Dimension of each action\n",
    "            fc1_units (int): Number of nodes in first hidden layer\n",
    "            fc2_units (int): Number of nodes in second hidden layer\n",
    "        '''\n",
    "        super(Actor, self).__init__()\n",
    "        self.fc1 = nn.Linear(state_size, fc1_units)\n",
    "        self.fc2 = nn.Linear(fc1_units, fc2_units)\n",
    "        self.fc3 = nn.Linear(fc2_units, action_size)\n",
    "        self.ln1 = nn.LayerNorm(fc1_units)\n",
    "        self.ln2 = nn.LayerNorm(fc2_units)\n",
    "        self.reset_parameters()\n",
    "\n",
    "    def reset_parameters(self):\n",
    "        self.fc1.weight.data.uniform_(*hidden_init(self.fc1))\n",
    "        self.fc2.weight.data.uniform_(*hidden_init(self.fc2))\n",
    "        self.fc3.weight.data.uniform_(-3e-3, 3e-3)\n",
    "\n",
    "    def forward(self, state):\n",
    "        '''Build an actor (policy) network that maps states -> actions'''\n",
    "        x = F.relu(self.fc1(state))\n",
    "        x = self.ln1(x)\n",
    "        x = F.relu(self.fc2(x))\n",
    "        x = self.ln2(x)\n",
    "        return torch.tanh(self.fc3(x))\n",
    "\n",
    "\n",
    "class Critic(nn.Module):\n",
    "    '''Critic (Value) Model'''\n",
    "\n",
    "    def __init__(self, state_size, action_size, fc1_units=128, fc2_units=256):\n",
    "        '''Initialize parameters and build model.\n",
    "        Params\n",
    "        ======\n",
    "            state_size (int): Dimension of each state\n",
    "            action_size (int): Dimension of each action\n",
    "            fc1_units (int): Number of nodes in the first hidden layer\n",
    "            fc2_units (int): Number of nodes in the second hidden layer\n",
    "            fc3_units (int): Number of nodes in the third hidden layer\n",
    "        '''\n",
    "        super(Critic, self).__init__()\n",
    "        self.fc1 = nn.Linear(state_size, fc1_units)\n",
    "        self.fc2 = nn.Linear(fc1_units + action_size, fc2_units)\n",
    "        self.fc3 = nn.Linear(fc2_units, 1)\n",
    "        self.ln1 = nn.LayerNorm(fc1_units)\n",
    "        self.ln2 = nn.LayerNorm(fc2_units)\n",
    "        self.reset_parameters()\n",
    "\n",
    "    def reset_parameters(self):\n",
    "        self.fc1.weight.data.uniform_(*hidden_init(self.fc1))\n",
    "        self.fc2.weight.data.uniform_(*hidden_init(self.fc2))\n",
    "        self.fc3.weight.data.uniform_(-3e-3, 3e-3)\n",
    "\n",
    "    def forward(self, state, action):\n",
    "        '''Build a critic (value) network that maps (state, action) pairs -> Q-values'''\n",
    "        x = F.leaky_relu(self.fc1(state))\n",
    "        x = self.ln1(x)\n",
    "        x = torch.cat((x, action), dim=1)\n",
    "        x = F.leaky_relu(self.fc2(x))\n",
    "        x = self.ln2(x)\n",
    "        return self.fc3(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "### Exploration: Adding Random Noise to the Continuous Actions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "code_folding": [
     0
    ],
    "deletable": false,
    "editable": false
   },
   "outputs": [],
   "source": [
    "class OUNoise:\n",
    "    '''Ornstein-Uhlenbeck process'''\n",
    "    \n",
    "    def __init__(self, size, mu=0.0, theta=0.15, sigma=0.1):\n",
    "        '''Initialize parameters and noise process'''\n",
    "        self.state = None\n",
    "        self.mu = mu * np.ones(size)\n",
    "        self.theta = theta\n",
    "        self.sigma = sigma\n",
    "        self.reset()\n",
    "\n",
    "    def reset(self):\n",
    "        '''Reset the internal state (= noise) to mean (mu)'''\n",
    "        self.state = copy.copy(self.mu)\n",
    "\n",
    "    def sample(self):\n",
    "        '''Update internal state and return it as a noise sample'''\n",
    "        x = self.state\n",
    "        dx = self.theta * (self.mu - x) + self.sigma * np.array([rand.random() for i in range(len(x))])\n",
    "        self.state = x + dx\n",
    "        return self.state"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "### Experience Replay Buffer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "code_folding": [
     0
    ],
    "deletable": false,
    "editable": false
   },
   "outputs": [],
   "source": [
    "class ReplayBuffer:\n",
    "    '''Fixed-size buffer to store experience tuples'''        \n",
    "\n",
    "    def __init__(self, action_size, buffer_size, batch_size):\n",
    "        '''Initialize a ReplayBuffer object.\n",
    "        Params\n",
    "        ======\n",
    "            action_size (int): number of actions\n",
    "            buffer_size (int): maximum size of buffer\n",
    "            batch_size (int): size of each training batch\n",
    "        '''        \n",
    "        self.action_size = action_size\n",
    "        self.memory = deque(maxlen=buffer_size)  # internal memory (deque)\n",
    "        self.batch_size = batch_size\n",
    "        self.experience = namedtuple('Experience', field_names=['state', 'action', 'reward', 'next_state', 'done'])\n",
    "\n",
    "    def add(self, state, action, reward, next_state, done):\n",
    "        '''Add a new experience to memory'''\n",
    "        e = self.experience(state, action, reward, next_state, done)\n",
    "        self.memory.append(e)\n",
    "    \n",
    "    def sample(self):\n",
    "        '''Randomly sample a batch of experiences from memory'''\n",
    "        experiences = rand.sample(self.memory, k=self.batch_size)\n",
    "\n",
    "        states = torch.from_numpy(np.vstack([e.state for e in experiences if e is not None])).float().to(device)\n",
    "        actions = torch.from_numpy(np.vstack([e.action for e in experiences if e is not None])).float().to(device)\n",
    "        rewards = torch.from_numpy(np.vstack([e.reward for e in experiences if e is not None])).float().to(device)\n",
    "        next_states = torch.from_numpy(np.vstack([e.next_state for e in experiences if e is not None])).float().to(device)\n",
    "        dones = torch.from_numpy(np.vstack([e.done for e in experiences if e is not None]).astype(np.uint8)).float().to(device)\n",
    "\n",
    "        return (states, actions, rewards, next_states, dones)\n",
    "    \n",
    "    def __len__(self):\n",
    "        '''Return the current size of internal memory'''\n",
    "        return len(self.memory)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "### Hyperparameters for Training"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "BUFFER_SIZE  = int(1e6)      # replay buffer size\n",
    "BATCH_SIZE   = 128           # minibatch size\n",
    "GAMMA        = 0.99          # discount factor\n",
    "TAU          = 3e-3          # for soft update of target parameters\n",
    "\n",
    "LR_ACTOR     = 1e-3          # learning rate of the actor \n",
    "LR_CRITIC    = 2 * LR_ACTOR  # learning rate of the critic [1, 10] times of LR_ACTOR\n",
    "WEIGHT_DECAY = 0.0001        # L2 weight decay [0, 0.0001]\n",
    "\n",
    "NOISE_MU     = 0.0\n",
    "NOISE_THETA  = 0.15\n",
    "NOISE_SIGMA  = 0.1\n",
    "\n",
    "TARGET_SCORE = 100"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "### The DDPG Agent\n",
    "\n",
    "The `learn` method in the `Agent` class does the actual learning. It uses sampled batch of experience tuples.\n",
    "\n",
    "Sometimes learning becomes unstable i.e. accuracy/score might suddenly drop after some short and steady progress. Clipping the gradient values might help in retaining stability of learning.\n",
    "\n",
    "```python\n",
    "optimizer.zero_grad()\n",
    "loss.backward()\n",
    "torch.nn.utils.clip_grad_norm_(model.parameters(), 1)\n",
    "optimizer.step()\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "code_folding": [
     0
    ],
    "deletable": false,
    "editable": false
   },
   "outputs": [],
   "source": [
    "class AgentDDPG():\n",
    "    '''Interacts with and learns from the environment'''        \n",
    "\n",
    "    def __init__(self, state_size, action_size):\n",
    "        '''Initialize an Agent object\n",
    "        \n",
    "        Params\n",
    "        ======\n",
    "            state_size (int): dimension of each state\n",
    "            action_size (int): dimension of each action\n",
    "        '''\n",
    "        \n",
    "        # Actor Network (w/ Target Network)\n",
    "        self.actor_local = Actor(state_size, action_size).to(device)\n",
    "        self.actor_target = Actor(state_size, action_size).to(device)\n",
    "        self.actor_optimizer = optim.Adam(self.actor_local.parameters(), lr=LR_ACTOR)\n",
    "\n",
    "        # Critic Network (w/ Target Network)\n",
    "        self.critic_local = Critic(state_size, action_size).to(device)\n",
    "        self.critic_target = Critic(state_size, action_size).to(device)\n",
    "        self.critic_optimizer = optim.Adam(self.critic_local.parameters(), lr=LR_CRITIC, weight_decay=WEIGHT_DECAY)\n",
    "\n",
    "        # Noise process\n",
    "        self.noise = OUNoise(action_size, mu=NOISE_MU, theta=NOISE_THETA, sigma=NOISE_SIGMA)\n",
    "\n",
    "        # Replay memory\n",
    "        self.memory = ReplayBuffer(action_size, BUFFER_SIZE, BATCH_SIZE)\n",
    "        \n",
    "        self.hard_update(self.actor_target, self.actor_local)\n",
    "        self.hard_update(self.critic_target, self.critic_local)\n",
    "            \n",
    "    def step(self, state, action, reward, next_state, done):\n",
    "        '''Save experience in replay memory, and use random sample from buffer to learn'''\n",
    "        # Save experience / reward\n",
    "        self.memory.add(state, action, reward, next_state, done)\n",
    "\n",
    "        # Learn, if enough samples are available in memory\n",
    "        if len(self.memory) > self.memory.batch_size:\n",
    "            experiences = self.memory.sample()\n",
    "            self.learn(experiences, GAMMA)\n",
    "\n",
    "    def act(self, state, add_noise=True):\n",
    "        '''Returns actions for given state as per current policy'''\n",
    "        state = torch.from_numpy(state).float().to(device)\n",
    "        self.actor_local.eval()\n",
    "        with torch.no_grad():\n",
    "            action = self.actor_local(state).cpu().numpy()\n",
    "        self.actor_local.train()\n",
    "        if add_noise:\n",
    "            action += self.noise.sample()\n",
    "        return np.clip(action, -1, 1)\n",
    "        # ----- if action value needs to be between [0,1] ----- #\n",
    "        # return np.clip((action + 1.0) / 2.0, 0, 1)\n",
    "\n",
    "    def reset(self):\n",
    "        self.noise.reset()\n",
    "\n",
    "    def learn(self, experiences, gamma):\n",
    "        '''Update policy and value parameters using given batch of experience tuples.\n",
    "        Q_targets = r + γ * critic_target(next_state, actor_target(next_state))\n",
    "        where:\n",
    "            actor_target(state) -> action\n",
    "            critic_target(state, action) -> Q-value\n",
    "\n",
    "        Params\n",
    "        ======\n",
    "            experiences (Tuple[torch.Tensor]): tuple of (s, a, r, s', done) tuples \n",
    "            gamma (float): discount factor\n",
    "        '''\n",
    "        states, actions, rewards, next_states, dones = experiences\n",
    "\n",
    "        # ---------------------------- update critic ---------------------------- #\n",
    "        # get predicted next-state actions and Q values from target models\n",
    "        with torch.no_grad():\n",
    "            target_next_actions = self.actor_target(next_states)\n",
    "            target_next_Q_values = self.critic_target(next_states, target_next_actions)\n",
    "        \n",
    "            # compute Q targets for current states (y_i)\n",
    "            td_target = rewards + (gamma * target_next_Q_values * (1 - dones))\n",
    "        \n",
    "        # compute Q values for the current states and actions\n",
    "        Q_expected = self.critic_local(states, actions)\n",
    "        \n",
    "        # compute critic loss\n",
    "        critic_loss = F.mse_loss(Q_expected, td_target.detach())\n",
    "\n",
    "        # minimize the loss\n",
    "        self.critic_optimizer.zero_grad()\n",
    "        critic_loss.backward()\n",
    "        \n",
    "        # optional gradient clipping sometimes helps in stable learning\n",
    "        torch.nn.utils.clip_grad_norm_(self.critic_local.parameters(), 1)\n",
    "        \n",
    "        self.critic_optimizer.step()\n",
    "\n",
    "        # ---------------------------- update actor ---------------------------- #   \n",
    "        actions = self.actor_local(states)\n",
    "        \n",
    "        # Compute actor loss\n",
    "        actor_loss = - self.critic_local(states, actions).mean()\n",
    "        \n",
    "        # Minimize the loss\n",
    "        self.actor_optimizer.zero_grad()\n",
    "        actor_loss.backward()\n",
    "        self.actor_optimizer.step()\n",
    "        \n",
    "        # ----------------------- update target networks ----------------------- #\n",
    "        self.soft_update(self.actor_target, self.actor_local, TAU)\n",
    "        self.soft_update(self.critic_target, self.critic_local, TAU)\n",
    "    \n",
    "    def hard_update(self, target_model, source_model):\n",
    "        for target_param, source_param in zip(target_model.parameters(), source_model.parameters()):\n",
    "            target_param.data.copy_(source_param.data)\n",
    "\n",
    "    def soft_update(self, target_model, source_model, tau):\n",
    "        '''Soft update model parameters\n",
    "        θ_target = τ*θ_local + (1 - τ)*θ_target\n",
    "\n",
    "        Params\n",
    "        ======\n",
    "            target_model: PyTorch model (weights will be copied to)\n",
    "            source_model: PyTorch model (weights will be copied from)\n",
    "            tau (float): interpolation parameter \n",
    "        '''\n",
    "        for target_param, source_param in zip(target_model.parameters(), source_model.parameters()):\n",
    "            target_param.data.copy_(target_param.data * (1.0 - tau) + source_param.data * tau)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "### Watch an Untrained Agent in Action"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "code_folding": [
     5
    ],
    "deletable": false,
    "editable": false
   },
   "outputs": [],
   "source": [
    "env = gym.make(ENVIRONMENT)\n",
    "agent = AgentDDPG(state_size=STATE_SIZE, action_size=ACTION_SIZE)\n",
    "\n",
    "state = env.reset()\n",
    "img = plt.imshow(env.render(mode='rgb_array'))\n",
    "for t in range(200):\n",
    "    action = agent.act(state, add_noise=False)\n",
    "    img.set_data(env.render(mode='rgb_array')) \n",
    "    plt.axis('off')\n",
    "    display.display(plt.gcf())\n",
    "    display.clear_output(wait=True)\n",
    "    state, reward, done, _ = env.step(action)\n",
    "    if done:\n",
    "        break\n",
    "\n",
    "env.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "### Train the Agent with DDPG"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "code_folding": [
     0
    ],
    "deletable": false,
    "editable": false
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   "outputs": [],
   "source": [
    "def train(n_episodes=1000, planning_horizon=300, print_every=50, save_every=100):\n",
    "    agent = AgentDDPG(state_size=STATE_SIZE, action_size=ACTION_SIZE)\n",
    "    start_episode = 0\n",
    "    scores = []\n",
    "    solved = False \n",
    "    if os.path.isfile(DDPG_MODEL_FILE):\n",
    "        # load training checkpoints from file\n",
    "        map_location = (lambda storage, loc: storage.cuda()) if torch.cuda.is_available() else 'cpu'\n",
    "        checkpoint = torch.load(DDPG_MODEL_FILE, map_location=map_location)\n",
    "        agent.actor_local.load_state_dict(checkpoint['actor_local'])\n",
    "        agent.actor_target.load_state_dict(checkpoint['actor_target'])\n",
    "        agent.actor_optimizer.load_state_dict(checkpoint['actor_optimizer'])\n",
    "        agent.critic_local.load_state_dict(checkpoint['critic_local'])\n",
    "        agent.critic_target.load_state_dict(checkpoint['critic_target'])\n",
    "        agent.critic_optimizer.load_state_dict(checkpoint['critic_optimizer'])\n",
    "        start_episode = checkpoint['episode']\n",
    "        scores = checkpoint['scores']\n",
    "        solved = checkpoint['solved']\n",
    "    if solved:\n",
    "        return scores    \n",
    "    agent.actor_local.train()\n",
    "    agent.critic_local.train()\n",
    "    env = gym.make(ENVIRONMENT)\n",
    "    scores_deque = deque(maxlen=100)\n",
    "    try:\n",
    "        for e in range(start_episode, start_episode + n_episodes):\n",
    "            state = env.reset()\n",
    "            agent.reset()\n",
    "            score = 0\n",
    "            for t in range(planning_horizon):\n",
    "                action = agent.act(state)\n",
    "                next_state, reward, done, _ = env.step(action)\n",
    "                agent.step(state, action, reward, next_state, done)\n",
    "                state = next_state\n",
    "                score += reward\n",
    "                if done:\n",
    "                    break \n",
    "            scores_deque.append(score)\n",
    "            scores.append(score)\n",
    "\n",
    "            # display progress after every iteration        \n",
    "            print('\\r' + ' ' * 120, end='')\n",
    "            print('\\rEpisode {}\\tAverage Score: {:.2f}\\tScore: {:.2f}'.format(e + 1, np.mean(scores_deque), score), end='')\n",
    "            if (e + 1) % print_every == 0:\n",
    "                print('\\r' + ' ' * 120, end='')\n",
    "                print('\\rEpisode {}\\tAverage Score: {:.2f}'.format(e + 1, np.mean(scores_deque)))\n",
    "            if (\n",
    "                (e == start_episode + n_episodes - 1) or\n",
    "                ((e + 1) % save_every == 0) or\n",
    "                np.mean(scores_deque) >= TARGET_SCORE\n",
    "            ):\n",
    "                torch.save({\n",
    "                    'episode': e + 1,\n",
    "                    'scores': scores,\n",
    "                    'solved': True if np.mean(scores_deque) >= TARGET_SCORE else False,\n",
    "                    'actor_local': agent.actor_local.state_dict(),\n",
    "                    'actor_target': agent.actor_target.state_dict(),\n",
    "                    'actor_optimizer': agent.actor_optimizer.state_dict(),\n",
    "                    'critic_local': agent.critic_local.state_dict(),\n",
    "                    'critic_target': agent.critic_target.state_dict(),\n",
    "                    'critic_optimizer': agent.critic_optimizer.state_dict()    \n",
    "                }, DDPG_MODEL_FILE)\n",
    "                if np.mean(scores_deque) >= TARGET_SCORE:\n",
    "                    print('\\nEnvironment solved in {:04d} episodes!\\tAverage Score: {:.4f}'.format(e + 1, np.mean(scores_deque)))\n",
    "                    break\n",
    "    except KeyboardInterrupt:\n",
    "        print('\\nTraining Interrupted')\n",
    "        env.close()\n",
    "        return scores\n",
    "    env.close()\n",
    "    return scores"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "Run the code cell below to train the agent from scratch. Try different values of the parameters in the function, to try to get better performance!\n",
    "\n",
    "```\n",
    "Pendulum-v0      : train()\n",
    "BipedalWalker-v3 : train(n_episodes=4000, planning_horizon=1000)\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "scores = train(n_episodes=4000, planning_horizon=1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "### Plot the Scores"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "deletable": false,
    "editable": false
   },
   "outputs": [],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "plt.plot(np.arange(1, len(scores)+1), scores)\n",
    "plt.ylabel('Score')\n",
    "plt.xlabel('Episode #')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "### Watch a Smart Agent in Action"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "code_folding": [
     11
    ],
    "deletable": false,
    "editable": false
   },
   "outputs": [],
   "source": [
    "env = gym.make(ENVIRONMENT)\n",
    "agent = AgentDDPG(state_size=STATE_SIZE, action_size=ACTION_SIZE)\n",
    "\n",
    "# load the weights from file\n",
    "map_location = (lambda storage, loc: storage.cuda()) if torch.cuda.is_available() else 'cpu'\n",
    "checkpoint = torch.load(DDPG_MODEL_FILE, map_location=map_location)\n",
    "agent.actor_local.load_state_dict(checkpoint['actor_local'])\n",
    "agent.actor_local.eval()\n",
    "\n",
    "# simulate the smart agent            \n",
    "state = env.reset()\n",
    "img = plt.imshow(env.render(mode='rgb_array'))\n",
    "while True:\n",
    "    action = agent.act(state, add_noise=False)\n",
    "    img.set_data(env.render(mode='rgb_array')) \n",
    "    plt.axis('off')\n",
    "    display.display(plt.gcf())\n",
    "    display.clear_output(wait=True)\n",
    "    state, reward, done, _ = env.step(action)\n",
    "    if done:\n",
    "        break \n",
    "        \n",
    "env.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "### Notes\n",
    "\n",
    "- Nudging the various hyperparameters and network architecture may help us solving the environments faster.\n",
    "- We may try **prioritized experience replay**, to see if that speeds up learning.  \n",
    "- The current implementation adds Ornsetein-Uhlenbeck noise to the action space.  However, it has been [shown](https://blog.openai.com/better-exploration-with-parameter-noise/) that adding noise to the parameters of the neural network policy can improve performance."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": false,
    "editable": false,
    "run_control": {
     "frozen": true
    }
   },
   "source": [
    "---\n",
    "\n",
    "Next: [Multi Agent Reinforcement Learning](./Multi%20Agent%20RL.ipynb)"
   ]
  }
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