demo12-reinforcement-learning.ipynb

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    "# Goal: Policy Gradients and the Gym Environment\n",
    "\n",
    "The goal of this demo is to get familiar with the [Gymansium](https://gymnasium.farama.org) library and implement REINFORCE, a policy gradient algorithm for Reinforcement Learning. In particular, we will use REINFORCE to solve the [CartPole](https://jeffjar.me/cartpole.html) environment provided by Gym. \n",
    "\n",
    "**Small note: we will be using OpenAI's [Gym Library](https://github.com/openai/gym#important-notice) rather than Gymnasium**\n",
    "\n",
    "Reinforcement Learning is fundmantally a problem in sequential decision making. The following diagram from the [seminal text in the field](http://incompleteideas.net/book/the-book-2nd.html) describes it well:\n",
    "\n",
    "![](http://www.incompleteideas.net/book/ebook/figtmp7.png)\n",
    "\n",
    "We have an *agent* that exists in some *environment*. At each timestep, the agent receives an observation that encapsulates the state of the environment (denoted as $s$) and takes an action $a$ based on this state. This mapping from states to actions is known as the agent's policy $\\pi$. After taking an action, the state of the environment is updated. \n",
    "\n",
    "Additionally at each time step, the agent will receive a reward signal $r$ from the environment. Thus the goal of our agent is to figure out the best policy where “best” is defined in terms of maximizing the rewards ([see class notes](https://chinmayhegde.github.io/dl-notes/notes/lecture09/#setup))."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "3rM2HQIICT4n"
   },
   "source": [
    "## Imports\n",
    "\n",
    "Let's begin by importing our favorite packages. We will also import `gym`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "EDc7Tt0GB_3x",
    "outputId": "c3cad9f5-988e-4aae-f0ae-485f85b4ee4e"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "import torch.nn as nn\n",
    "import torch.optim as optim\n",
    "import torch.nn.functional as F\n",
    "import torch.distributions as distributions\n",
    "\n",
    "import gym\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "print(torch.cuda.is_available())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "rd7Pjk_ItcML"
   },
   "source": [
    "We will also import turn off deprecation warnings since we are using a slighly outdated library."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "id": "W_j6k0-BhOS8"
   },
   "outputs": [],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\", category=DeprecationWarning)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "6_jpJAnehNnG"
   },
   "source": [
    "## The CartPole-v1 Environment\n",
    "\n",
    "Let's instantiate the `CartPole-v1` environment. We can render what our CartPole environment looks like. The environment will remain static unless we call `env.step()`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 413
    },
    "id": "izi2PM72sRBe",
    "outputId": "cb55e1b0-26e8-44d5-f86f-3919e3198558"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f93f913f880>"
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     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "env = gym.make(\"CartPole-v1\")\n",
    "env.reset()\n",
    "plt.imshow(env.render(mode='rgb_array'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "hNLNtnHg5unk"
   },
   "source": [
    "So we can see that we have a pole attached to a cart that can move in the x-direction. And our goal is to keep the pole upright."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Aj5aalWnhWn3"
   },
   "source": [
    "## What are the actions, states, reward function for CartPole-v1?\n",
    "Now, let's concretize our understanding by looking at the action, state, and reward space. As we go through this section, do a sanity check with the [CartPole-v1 documentation](https://gymnasium.farama.org/environments/classic_control/cart_pole/). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "t7Ymu9dy6keI"
   },
   "source": [
    "### [Action Space](https://gymnasium.farama.org/environments/classic_control/cart_pole/#action-space)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "hgyvVGCKsuCn",
    "outputId": "d0cba40d-29f1-454f-a7d8-a55426ee0592"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Discrete(2)\n"
     ]
    }
   ],
   "source": [
    "print(env.action_space)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "RB3sKsQ66pJd"
   },
   "source": [
    "So, our action space consists of two discrete decisions: move left (0) or move right (1). We can perform a uniform sample over the action space directly from `env`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "5owyVUwO60Gi",
    "outputId": "4c910551-789c-4539-f8d7-0cf3eaa5fd26"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Uniformly choosing an action: 0\n"
     ]
    }
   ],
   "source": [
    "print(\"Uniformly choosing an action:\", env.action_space.sample())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "kXmXr7EN6491"
   },
   "source": [
    "Try running the above cell a few times. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ndvTNrSg69YZ"
   },
   "source": [
    "### [Observation (State) Space](https://gymnasium.farama.org/environments/classic_control/cart_pole/#observation-space)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "pwV6gLF8tCfg",
    "outputId": "0ebcd6c3-1629-4de5-b115-bcc0c0ba65e3"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(4,)\n"
     ]
    }
   ],
   "source": [
    "print(env.observation_space.shape) # state space"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "JkPii7iX7Cpe"
   },
   "source": [
    "Our `state` will consist of four items:\n",
    "- the cart position\n",
    "- the cart velocity\n",
    "- the pole angle\n",
    "- the pole's angular velocity\n",
    "\n",
    "These are continuous variables and some of them are bounded. We can print out the bounds like so:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "kiCefTxd7LXd",
    "outputId": "db10f5fb-31cc-4734-f6b6-e4cbddc07b6c"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Box([-4.8000002e+00 -3.4028235e+38 -4.1887903e-01 -3.4028235e+38], [4.8000002e+00 3.4028235e+38 4.1887903e-01 3.4028235e+38], (4,), float32)\n"
     ]
    }
   ],
   "source": [
    "print(env.observation_space)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "QbA901g37Xle"
   },
   "source": [
    "### [Reward](https://gymnasium.farama.org/environments/classic_control/cart_pole/#rewards)\n",
    "\n",
    "We just receive a reward of `+1` for every time step until our pole falls over. If we keep the pole upright for more than 475 timesteps, that means we have solved the CartPole-v1 environent.\n",
    "\n",
    "\n",
    "### A Random Policy $\\pi$\n",
    "Let's create a random policy $\\pi$ that simply takes a random action at each timestep. We will play for a maximum of 500 timesteps and if we crash, we will break out of our loop."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "b97nEnznteAO",
    "outputId": "99d10497-7491-4c45-dcca-f31dcd67bca1"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "number of steps before we crashed: 17\n"
     ]
    }
   ],
   "source": [
    "rewards = []\n",
    "for idx in range(500):\n",
    "   action = env.action_space.sample()                # return either a 0 (for move left) or a 1 (for move right)\n",
    "   state, reward, terminated, _  = env.step(action)  # performs the action in our environment.\n",
    "   rewards.append(reward)\n",
    "   if terminated:\n",
    "     break\n",
    "print(\"number of steps before we crashed:\", idx)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "DJCh3ceC8JP1"
   },
   "source": [
    "So we made it 17 timesteps before our pole fell over! Let's visualize and print the final state of our environment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 413
    },
    "id": "LnxMOzKgt6mR",
    "outputId": "fb4de8e2-a769-41e4-860f-4d4b4ff3ee2b"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f93f85a4c70>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(env.render(mode='rgb_array'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ShixvRmf8Yuc"
   },
   "source": [
    "Check the [termination rules](https://gymnasium.farama.org/environments/classic_control/cart_pole/#episode-end) for CartPole to understand why our episode terminated."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "olpur-0it9QQ",
    "outputId": "0198316c-b49c-47c6-87e8-d01af86a233b"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.08003918  0.84610975 -0.21306242 -1.6377889 ]\n"
     ]
    }
   ],
   "source": [
    "print(state)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "kwS3VJ2fuCgu",
    "outputId": "944e5e13-ab7c-4431-a5ef-37eabe5972b2"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Degree of pole: -12.207577438843742\n"
     ]
    }
   ],
   "source": [
    "print(\"Degree of pole:\", np.rad2deg(-0.21306242))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "HmrMzCrw8gTd"
   },
   "source": [
    "Let's calculate our cumulative reward for our episode. It's common to sum the individual rewards starting at time step and discounting future rewards as follows:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "X2yaAu8Bue-W"
   },
   "source": [
    "$R = r_0 + \\gamma r_1 + \\gamma^2 r_2 \\ldots$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "cwAmhF-VusQU",
    "outputId": "a36fe8ac-fc64-4689-916b-ed34457fa8f6"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]\n"
     ]
    }
   ],
   "source": [
    "print(rewards)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "jgcqaSLoA65b"
   },
   "source": [
    "We will set our discount factor to $\\gamma=0.9$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "2foJSCQbuvT_",
    "outputId": "1b4971c9-441f-4a13-fe4a-f5399a9d8e5b"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8.499053647030008\n"
     ]
    }
   ],
   "source": [
    "R = 0\n",
    "gamma = 0.9\n",
    "for i in range(len(rewards)):\n",
    "  R += rewards[i] * gamma**i\n",
    "\n",
    "print(R)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "6JOIVpjN8yKx"
   },
   "source": [
    "So, it looks like we achieved a cumulative, discounted reward of 8.499. If we had solved the CartPole-v1 environment, we should have achieved a cumulative, discounted reward in the 400s!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "NQNYL0cthc4w"
   },
   "source": [
    "## Building a Policy Network\n",
    "\n",
    "Let's now build a policy network and use the REINFORCE algorithm to solve the CartPole-v1 environment. First, we will instantiate two CartPole-v1 environments: one for training and one for evaluation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "id": "TT4JRIm_u_pm"
   },
   "outputs": [],
   "source": [
    "train_env = gym.make('CartPole-v1')\n",
    "test_env  = gym.make('CartPole-v1')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "q3iE7T919gF8"
   },
   "source": [
    "Recall that our goal is to create a policy $\\pi$ that maps states to actions. We will use a small neural network for this."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "qgy4IUqlvP7d"
   },
   "source": [
    "$\\pi(a|s) = P[A = a | S = s]$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "id": "ZvHbxyl1wDRT"
   },
   "outputs": [],
   "source": [
    "class PolicyNet(nn.Module):\n",
    "  def __init__(self, state_space_size, hidden_dim, action_space_size, dropout=.5):\n",
    "    super().__init__()\n",
    "    self.net = nn.Sequential(\n",
    "        nn.Linear(state_space_size, hidden_dim), # 4 -> hidden_dim\n",
    "        nn.Dropout(dropout),\n",
    "        nn.ReLU(),\n",
    "        nn.Linear(hidden_dim, action_space_size) # hidden_dim -> 2\n",
    "    )\n",
    "\n",
    "  def forward(self, x):\n",
    "    return self.net(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "mubY7aFj90NS"
   },
   "source": [
    "Let's obtain the input and output dimensions of the policy network. We already know these values since we understand our environment but it's best to be Pythonic. We will also set the hidden dimension size here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "KdjoQ1Q3wXTG",
    "outputId": "d3052d0a-89ef-44fb-8954-612ce50a8e05"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "input dim: 4\n",
      "output dim: 2\n"
     ]
    }
   ],
   "source": [
    "input_dim = train_env.observation_space.shape[0]\n",
    "print('input dim:', input_dim)\n",
    "\n",
    "output_dim = train_env.action_space.n\n",
    "print('output dim:', output_dim)\n",
    "\n",
    "hidden_dim = 128"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "DhhoDQhR-DLv"
   },
   "source": [
    "Let's instantiate both the network and the optimizer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "1NyIGPmtwc65",
    "outputId": "ee11d1f5-a295-49bd-98dc-d563949a3fb9"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PolicyNet(\n",
      "  (net): Sequential(\n",
      "    (0): Linear(in_features=4, out_features=128, bias=True)\n",
      "    (1): Dropout(p=0.5, inplace=False)\n",
      "    (2): ReLU()\n",
      "    (3): Linear(in_features=128, out_features=2, bias=True)\n",
      "  )\n",
      ")\n"
     ]
    }
   ],
   "source": [
    "policy = PolicyNet(input_dim, hidden_dim, output_dim)\n",
    "print(policy)\n",
    "\n",
    "optimizer = optim.Adam(policy.parameters(), lr=0.01)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "tVgL0MNo9ykS"
   },
   "source": [
    "As it stand now, our policy network output a vector of size 2 which contains real values. We need to convert this to a proper probability distribution over two discrete outcomes. To do this, we will \n",
    "- normalize our output\n",
    "- convert this normalized vector to a torch distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "-mDea6VN-VOI"
   },
   "source": [
    "The following code snippet shows how we can do this."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "UBIPgCUawtda",
    "outputId": "323d2e78-55c3-4b3c-f6e8-3527fe272052"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "output: tensor([ 1.1884, -0.2575])\n",
      "probs: tensor([0.8094, 0.1906])\n",
      "Categorical(probs: torch.Size([2]))\n",
      "sample: tensor(0)\n",
      "log probl: tensor(-0.2115)\n"
     ]
    }
   ],
   "source": [
    "output = torch.randn(2,)                   # output of network\n",
    "print(\"output:\", output)\n",
    "probs = F.softmax(output, dim=-1)          # normalize using softmax\n",
    "print(\"probs:\", probs)\n",
    "dist = distributions.Categorical(probs)    # convert to discrete distribution\n",
    "print(dist)\n",
    "sample = dist.sample()                     # sample from our distribution\n",
    "print(\"sample:\", sample)\n",
    "print('log probl:', dist.log_prob(sample)) # find the log_prob of our sample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "y0Ib7reCxyKU",
    "outputId": "b586fbdf-d28e-455f-fdfb-597954a9c626"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.21146204654037185"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.log(0.8094)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "qiGnLvmg-ZS-"
   },
   "source": [
    "You will see that we also measured the log probability of our sample in the above code snippet. We will need to calculate the log probability for the REINFORCE algorithm."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "HXIK3tEbhf_L"
   },
   "source": [
    "## REINFORCE Algorithm (from [class notes](https://chinmayhegde.github.io/dl-notes/notes/lecture09/#policy-gradients))\n",
    "\n",
    "The following is the REINFORCE algorithm covered in class. I'd highly suggest going over the class notes to understand how the log-derivative trick is employed.\n",
    "\n",
    "- Sample a trajectory/rollout $(s_0,a_0, s_1, a_1, \\ldots, s_T, a_T)$\n",
    "- For each $t=0, 1, \\ldots, T-1$:\n",
    "  - Compute $R_t = r_t + \\gamma r_{t+1} + \\gamma^2 r_{t+2} $\n",
    "  - $\\theta \\leftarrow \\theta + \\eta R_t \\frac{d}{d\\theta}log\\left(\\pi(a_t|s_t)\\right)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "zuIgaVkbhkL5"
   },
   "source": [
    "## Calculating the Return for an Episode"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "bjI5DO0s--ec"
   },
   "source": [
    "In class, we described how to compute a single discounted reward of a trajectory. In practice, we want to leverage our data for more updates. We do this by considering the future discounted reward for *every* state in our trajectory."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "id": "YFF8mTVTyBLZ"
   },
   "outputs": [],
   "source": [
    "def calculate_returns(rewards, discount_factor, normalize=True):\n",
    "  returns = []\n",
    "  R = 0\n",
    "  for r in reversed(rewards):\n",
    "    R = r + R * discount_factor\n",
    "    returns.insert(0,R)\n",
    "\n",
    "    \n",
    "  returns = torch.tensor(returns)\n",
    "  # Remember we normalize to differentiate between\n",
    "  # \"good\" and \"bad\" actions\n",
    "  if normalize:\n",
    "    returns = (returns - returns.mean()) / returns.std()\n",
    "  \n",
    "  return returns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "iKehax23_CRD"
   },
   "source": [
    "Let's go ahead and run this cell for the rewards we obtained during our random policy run."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "gaIiaHTzyIp8",
    "outputId": "26ab9be6-afb7-4dbd-df0d-03617a2a0cf8"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([8.4991, 8.3323, 8.1470, 7.9411, 7.7123, 7.4581, 7.1757, 6.8619, 6.5132,\n",
       "        6.1258, 5.6953, 5.2170, 4.6856, 4.0951, 3.4390, 2.7100, 1.9000, 1.0000])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "calculate_returns(rewards, 0.9, False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "fKRkQEJv_MgN"
   },
   "source": [
    "Note that the first value in our `returns` tensor is the same value we calculated above (8.499)! Each value in the `returns` tensor calculates the discounted reward *starting from that time step and up to the end of the episode*. It's common to normalize the returns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "_2jhhLd7ylWp",
    "outputId": "c775e0a7-0898-4db2-f45b-c004f399cc1e"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([ 1.1837,  1.1119,  1.0321,  0.9434,  0.8449,  0.7354,  0.6138,  0.4786,\n",
       "         0.3285,  0.1616, -0.0237, -0.2297, -0.4586, -0.7129, -0.9955, -1.3094,\n",
       "        -1.6583, -2.0459])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "calculate_returns(rewards, 0.9, True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "AFRxYrY-hnOL"
   },
   "source": [
    "## Gradient Calculation\n",
    "Once we have returns and log probabilities of the actions we take, we will compute the loss and optimize. Note the negative sign in this `loss` expression. Can you see why we need to add the negative sign?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "id": "VqGSq5IGykDi"
   },
   "outputs": [],
   "source": [
    "def update_policy(returns, log_prob_actions, optimizer):\n",
    "  returns = returns.detach()\n",
    "  # Because we minimize (by convention) and we actually\n",
    "  # want to maximize returns, we negate the expected sum\n",
    "  loss = - (returns * log_prob_actions).sum()\n",
    "  optimizer.zero_grad()\n",
    "\n",
    "  loss.backward()\n",
    "  optimizer.step()\n",
    "\n",
    "  return loss.item()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "AnmnOO23hqIg"
   },
   "source": [
    "# Training Function\n",
    "\n",
    "Now we write the training and evaluation functions. Notice how training in RL is more involved than our standard applications.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "id": "8aMRM2Wty4xi"
   },
   "outputs": [],
   "source": [
    "def train(env, policy, optimizer, discount_factor=.99):\n",
    "  policy.train()\n",
    "  \n",
    "  log_prob_actions = []\n",
    "  rewards = []\n",
    "  done = False\n",
    "  episode_reward = 0\n",
    "\n",
    "  state = env.reset()\n",
    "\n",
    "  while not done:\n",
    "    state = torch.FloatTensor(state).unsqueeze(0)\n",
    "    action_pred = policy(state)\n",
    "    action_prob = F.softmax(action_pred, dim = -1) # normalize our output\n",
    "\n",
    "    dist = distributions.Categorical(action_prob)\n",
    "    action = dist.sample() # we sample (rather than take the best)\n",
    "    log_prob_action = dist.log_prob(action)\n",
    "\n",
    "    state, reward, done, _ = env.step(action.item())\n",
    "\n",
    "    log_prob_actions.append(log_prob_action)\n",
    "    rewards.append(reward)\n",
    "\n",
    "    episode_reward += reward\n",
    "  \n",
    "  log_prob_actions = torch.cat(log_prob_actions)\n",
    "  returns = calculate_returns(rewards, discount_factor)\n",
    "  loss = update_policy(returns, log_prob_actions, optimizer)\n",
    "\n",
    "  return loss, episode_reward"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "J4gjo4J_hsnO"
   },
   "source": [
    "# Evaluation Function\n",
    "\n",
    "The evaluation loop is similar expect we take the best action (i.e. the action that leads to the highest cumulative, discounted reward)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "id": "wz0KCd0Bhs9_"
   },
   "outputs": [],
   "source": [
    "def evaluate(env, policy, return_frames=False):\n",
    "  policy.eval()\n",
    "\n",
    "  done = False\n",
    "  episode_reward = 0\n",
    "  state = env.reset()\n",
    "  frames = []\n",
    "\n",
    "  while not done:\n",
    "    if return_frames:\n",
    "      frames += [env.render(mode='rgb_array')]\n",
    "    state = torch.FloatTensor(state).unsqueeze(0)\n",
    "\n",
    "    action_pred = policy(state)\n",
    "    action_prob = F.softmax(action_pred, dim=-1)\n",
    "\n",
    "    action = torch.argmax(action_prob, dim=-1) # we take the best\n",
    "    state, reward, done, _ = env.step(action.item())\n",
    "    episode_reward += reward\n",
    "  \n",
    "  if return_frames:\n",
    "    return episode_reward, frames\n",
    "  return episode_reward"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "XvfWQj1K_0Mw"
   },
   "source": [
    "Let's evaluate our untrained policy network in our `test_env`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "zTP4pZ1Lzp7K",
    "outputId": "6f518139-b99d-48b8-daed-06721cfbb520"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "11.0"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "evaluate(test_env, policy)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "gSBGbg4oADSz"
   },
   "source": [
    "## Training\n",
    "\n",
    "Now we're ready to train. Notice the very jagged nature of the loss history. This is because RL is different from our regular training: our policy is stochastic and the reward is more \"sparse\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "Mbu_ZluTzwr_",
    "outputId": "bfeabe10-42ec-491c-dd9c-d56fc88f9aaf"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "| Episode:  10 | Mean Train Rewards:  19.9 | Mean Test Rewards:  25.2 |\n",
      "| Episode:  20 | Mean Train Rewards:  24.9 | Mean Test Rewards:  67.4 |\n",
      "| Episode:  30 | Mean Train Rewards:  37.6 | Mean Test Rewards:  90.2 |\n",
      "| Episode:  40 | Mean Train Rewards:  54.1 | Mean Test Rewards: 113.6 |\n",
      "| Episode:  50 | Mean Train Rewards:  66.6 | Mean Test Rewards: 112.8 |\n",
      "| Episode:  60 | Mean Train Rewards:  74.0 | Mean Test Rewards: 136.2 |\n",
      "| Episode:  70 | Mean Train Rewards:  87.6 | Mean Test Rewards: 254.0 |\n",
      "| Episode:  80 | Mean Train Rewards:  97.4 | Mean Test Rewards: 334.6 |\n",
      "| Episode:  90 | Mean Train Rewards: 126.6 | Mean Test Rewards: 373.3 |\n",
      "| Episode: 100 | Mean Train Rewards: 157.4 | Mean Test Rewards: 380.4 |\n",
      "| Episode: 110 | Mean Train Rewards: 148.5 | Mean Test Rewards: 315.2 |\n",
      "| Episode: 120 | Mean Train Rewards: 198.8 | Mean Test Rewards: 313.5 |\n",
      "| Episode: 130 | Mean Train Rewards: 310.8 | Mean Test Rewards: 369.7 |\n",
      "Reached reward threshold in 138 episodes\n"
     ]
    }
   ],
   "source": [
    "max_episodes = 500\n",
    "num_trials = 25\n",
    "reward_threshold = 475\n",
    "print_every = 10\n",
    "\n",
    "train_rewards = []\n",
    "test_rewards = []\n",
    "\n",
    "for episode in range(1, max_episodes+1):\n",
    "  loss, train_reward = train(train_env, policy, optimizer)\n",
    "  test_reward = evaluate(test_env, policy)\n",
    "\n",
    "  train_rewards += [train_reward]\n",
    "  test_rewards += [test_reward]\n",
    "\n",
    "  mean_train_rewards = np.mean(train_rewards[-num_trials:])\n",
    "  mean_test_rewards = np.mean(test_rewards[-num_trials:])\n",
    "\n",
    "  if episode % print_every == 0:    \n",
    "    print(f'| Episode: {episode:3} | Mean Train Rewards: {mean_train_rewards:5.1f} | Mean Test Rewards: {mean_test_rewards:5.1f} |')\n",
    "    \n",
    "  if mean_test_rewards >= reward_threshold:\n",
    "    print(f'Reached reward threshold in {episode} episodes')\n",
    "    break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 710
    },
    "id": "2fjvhy01z71t",
    "outputId": "04b77224-1682-4cc8-ded1-3e3b9e06a624"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,8))\n",
    "plt.plot(test_rewards, label='Test Reward')\n",
    "plt.plot(train_rewards, label='Train Reward')\n",
    "plt.xlabel('Episode', fontsize=20)\n",
    "plt.ylabel('Reward', fontsize=20)\n",
    "plt.hlines(reward_threshold, 0, len(test_rewards), color='r')\n",
    "plt.legend(loc='lower right')\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "BFxNQBllAlid"
   },
   "source": [
    "And that's it! We went over the basic setup of Reinforcement Learning, talked about the gym environment, and used the REINFORCE algorithm to solve the cartpole environment."
   ]
  }
 ],
 "metadata": {
  "accelerator": "GPU",
  "colab": {
   "provenance": []
  },
  "gpuClass": "standard",
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}