Reinforcement (Q-)Learning with PyTorch.ipynb

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    "# PyTorch DQN tutorial\n",
    "\n",
    "This tutorial shows how to use PyTorch to train a DQN agent on the CartPole-v0 task from the [OpenAI Gym](https://gym.openai.com/).\n",
    "\n",
    "### Task\n",
    "\n",
    "The agent has to decide between two actions - moving the cart left or right - so that the pole attached to it stays upright. You can find an official leaderboard with various algorithms and visualizations at the [Gym website](https://gym.openai.com/envs/CartPole-v0).\n",
    "\n",
    "![cartpole](images/cartpole.gif)\n",
    "\n",
    "As the agent observes the current state of the environment and chooses an action, the environment *transitions* to a new state, and also returns a reward that indicates the consequences of the action. In this task, the environment terminates if the pole falls over too far.\n",
    "\n",
    "The CartPole task is designed so that the inputs to the agent are 4 real values representing the environment state (position, velocity, etc.). However, neural networks can solve the task purely by looking at the scene, so we'll use a patch of the screen centered on the cart as an input. Because of this, our results aren't directly comparable to the ones from the official leaderboard - our task is much harder. Unfortunately this does slow down the training, because we have to render all the frames.\n",
    "\n",
    "Strictly speaking, we will present the state as the difference between the current screen patch and the previous one. This will allow the agent to take the velocity of the pole into account from one image."
   ]
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    "### Packages\n",
    "\n",
    "First, let's import needed packages. Firstly, we need [`gym`](https://gym.openai.com/docs) for the environment. We'll also use the following from PyTorch:\n",
    "\n",
    "* neural networks (`torch.nn`)\n",
    "* optimization (`torch.optim`)\n",
    "* automatic differentiation (`torch.autograd`)\n",
    "* utilities for vision tasks (`torchvision` - [a separate package](https://github.com/pytorch/vision))."
   ]
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  {
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   "source": [
    "import gym\n",
    "import math\n",
    "import random\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from collections import namedtuple\n",
    "from itertools import count\n",
    "from copy import deepcopy\n",
    "from PIL import Image\n",
    "\n",
    "import torch\n",
    "import torch.nn as nn\n",
    "import torch.optim as optim\n",
    "import torch.autograd as autograd\n",
    "import torch.nn.functional as F\n",
    "import torchvision.transforms as T\n",
    "\n",
    "env = gym.make('CartPole-v0')\n",
    "env = env.unwrapped"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
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   "source": [
    "from IPython import display\n",
    "%matplotlib inline"
   ]
  },
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   "metadata": {},
   "source": [
    "### Replay Memory\n",
    "\n",
    "We'll be using experience replay memory for training our DQN. It stores the transitions that the agent observes, allowing us to reuse this data later. By sampling from it randomly, the transitions that build up a batch are decorrelated. It has been shown that this greatly stabilizes and improves the DQN training procedure.\n",
    "\n",
    "For this, we're going to need two classses:\n",
    "\n",
    "* `Transition` - a named tuple representing a single transition in our environment\n",
    "* `ReplayMemory` - a cyclic buffer of bounded size that holds the transitions observed recently. It also implements a `.sample()` method for selecting a random batch of transitions for training."
   ]
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   "source": [
    "Transition = namedtuple('Transition', ('state', 'action', 'next_state', 'reward'))\n",
    "\n",
    "class ReplayMemory(object):\n",
    "    \n",
    "    def __init__(self, capacity):\n",
    "        self.capacity = capacity\n",
    "        self.memory = []\n",
    "        self.position = 0\n",
    "        \n",
    "    def push(self, *args):\n",
    "        \"\"\"Saves a transition.\"\"\"\n",
    "        if len(self.memory) < self.capacity:\n",
    "            self.memory.append(None) \n",
    "        self.memory[self.position] = Transition(*args)\n",
    "        self.position = (self.position + 1) % self.capacity\n",
    "        \n",
    "    def sample(self, batch_size):\n",
    "        return random.sample(self.memory, batch_size)\n",
    "    \n",
    "    def __len__(self):\n",
    "        return len(self.memory)"
   ]
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   "source": [
    "Now, let's define our model. But first, let quickly recap what a DQN is.\n",
    "\n",
    "### DQN algorithm\n",
    "\n",
    "Our environment is deterministic, so all equations presented here are also formulated deterministically for the sake of simplicity. In the reinforcement learning literature, they would also contain expectations over stochastic transitions in the environment.\n",
    "\n",
    "Our aim will be to train a policy that tries to maximize the discounted, cumulative reward $R_{t_0} = \\sum_{t=t_0}^{\\infty} \\gamma^{t - t_0} r_t$, where $R_{t_0}$ is also known as the *return*. The discount, $\\gamma$, should be a constant between $0$ and $1$ that ensures the sum converges. It makes rewards from the uncertain far future less important for our agent than the ones in the near future that it can be fairly confident about.\n",
    "\n",
    "The main idea behind Q-learning is that if we had a function $Q^*: State \\times Action \\rightarrow \\mathbb{R}$, that could tell us what our return would be, if we were to take an action in a given state, then we could easily construct a policy that maximizes our rewards:\n",
    "\n",
    "$$\\pi^*(s) = \\arg\\!\\max_a \\ Q^*(s, a)$$\n",
    "\n",
    "However, we don't know everything about the world, so we don't have access to $Q^*$. But, since neural networks are universal function approximators, we can simply create one and train it to resemble $Q^*$.\n",
    "\n",
    "For our training update rule, we'll use a fact that every $Q$ function for some policy obeys the Bellman equation:\n",
    "\n",
    "$$Q^{\\pi}(s, a) = r + \\gamma Q^{\\pi}(s', \\pi(s'))$$\n",
    "\n",
    "The difference between the two sides of the equality is known as the temporal difference error, $\\delta$:\n",
    "\n",
    "$$\\delta = Q(s, a) - (r + \\gamma \\max_a Q(s', a))$$\n",
    "\n",
    "To minimise this error, we will use the [Huber loss](https://en.wikipedia.org/wiki/Huber_loss). The Huber loss acts like the mean squared error when the error is small, but like the mean absolute error when the error is large - this makes it more robust to outliers when the estimates of $Q$ are very noisy. We calculate this over a batch of transitions, $B$, sampled from the replay memory:\n",
    "\n",
    "$$\\mathcal{L} = \\frac{1}{|B|}\\sum_{(s, a, s', r) \\ \\in \\ B} \\mathcal{L}(\\delta) \\quad \\text{where} \\quad \\mathcal{L}(\\delta) = \\begin{cases}\n",
    "  \\frac{1}{2}{\\delta^2}  & \\text{for } |\\delta| \\le 1, \\\\\n",
    "  |\\delta| - \\frac{1}{2} & \\text{otherwise.}\n",
    "\\end{cases}$$\n",
    "\n",
    "### Q-network\n",
    "\n",
    "Our model will be a convolutional neural network that takes in the difference between the current and previous screen patches. It has two outputs, representing $Q(s, \\mathrm{left})$ and $Q(s, \\mathrm{right})$ (where $s$ is the input to the network). In effect, the network is trying to predict the *quality* of taking each action given the current input."
   ]
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   "source": [
    "class DQN(nn.Module):\n",
    "    def __init__(self):\n",
    "        super(DQN, self).__init__()\n",
    "        self.conv1 = nn.Conv2d(3, 16, kernel_size=5, stride=2)\n",
    "        self.bn1 = nn.BatchNorm2d(16)\n",
    "        self.conv2 = nn.Conv2d(16, 32, kernel_size=5, stride=2)\n",
    "        self.bn2 = nn.BatchNorm2d(32)\n",
    "        self.conv3 = nn.Conv2d(32, 32, kernel_size=5, stride=2)\n",
    "        self.bn3 = nn.BatchNorm2d(32)\n",
    "        self.head = nn.Linear(448, 2)\n",
    "        \n",
    "    def forward(self, x):\n",
    "        x = F.relu(self.bn1(self.conv1(x)))\n",
    "        x = F.relu(self.bn2(self.conv2(x)))\n",
    "        x = F.relu(self.bn3(self.conv3(x)))\n",
    "        return self.head(x.view(x.size(0), -1))"
   ]
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   "cell_type": "markdown",
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   "source": [
    "### Input extraction\n",
    "\n",
    "The code below are utilities for extracting and processing rendered images from the environment. It uses the `torchvision` package, which makes it easy to compose image transforms. Once you run the cell it will display an example patch that it extracted."
   ]
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   "source": [
    "resize = T.Compose([T.ToPILImage(), T.Scale(40, interpolation=Image.CUBIC), T.ToTensor()])\n",
    "\n",
    "# This is based on the code from gym.\n",
    "screen_width = 600\n",
    "def get_cart_location():\n",
    "    world_width = env.x_threshold * 2\n",
    "    scale = screen_width / world_width\n",
    "    return int(env.state[0] * scale + screen_width / 2.0) # MIDDLE OF CART\n",
    "    \n",
    "    \n",
    "def get_screen():\n",
    "    screen = env.render(mode='rgb_array').transpose((2, 0, 1)) # transpose into torch order (CHW)\n",
    "    # Strip off the top and bottom of the screen\n",
    "    screen = screen[:, 160:320]\n",
    "    view_width = 320\n",
    "    cart_location = get_cart_location()\n",
    "    if cart_location < view_width // 2:\n",
    "        slice_range = slice(view_width)\n",
    "    elif cart_location > (screen_width - view_width // 2):\n",
    "        slice_range = slice(-view_width,None)\n",
    "    else:\n",
    "        slice_range = slice(cart_location - view_width // 2, cart_location + view_width // 2)\n",
    "    # Strip off the edges, so that we have a square image centered on a cart\n",
    "    screen = screen[:, :, slice_range]\n",
    "    # Convert to float, rescare, convert to torch tensor (this doesn't require a copy)\n",
    "    screen = np.ascontiguousarray(screen, dtype=np.float32) / 255\n",
    "    screen = torch.from_numpy(screen)\n",
    "    # Resize, and add a batch dimension (BCHW)\n",
    "    return resize(screen).unsqueeze(0)\n",
    "\n",
    "env.reset()\n",
    "plt.imshow(get_screen().squeeze(0).permute(1, 2, 0).numpy(), interpolation='none')\n",
    "plt.show()"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Training hyperparameters and utilities\n",
    "\n",
    "This cell instantiates our model and its optimizer, and defines some utilities:\n",
    "\n",
    "* `Variable` - this is a simple wrapper around `torch.autograd.Variable` that will automatically send the data to the GPU every time we construct a Variable.\n",
    "* `select_action` - will select an action accordingly to an epsilon greedy policy. Simply put, we'll sometimes use our model for choosing the action, and sometimes we'll just sample one uniformly. The probability of choosing a random action will start at `EPS_START` and will decay exponentially towards `EPS_END`. `EPS_DECAY` controls the rate of the decay.\n",
    "* `plot_durations` - a helper for plotting the durations of episodes, along with an average over the last 100 episodes (the measure used in the official evaluations). The plot will be underneath the cell containing the main training loop, and will update after every episode."
   ]
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    "BATCH_SIZE = 128\n",
    "GAMMA = 0.999\n",
    "EPS_START = 0.9\n",
    "EPS_END = 0.05\n",
    "EPS_DECAY = 200\n",
    "dtype = torch.cuda.FloatTensor if torch.cuda.is_available() else torch.FloatTensor\n",
    "\n",
    "model = DQN()\n",
    "memory = ReplayMemory(10000)\n",
    "optimizer = optim.RMSprop(model.parameters())\n",
    "\n",
    "model.type(dtype)\n",
    "\n",
    "\n",
    "steps_done = 0\n",
    "def select_action(state):\n",
    "    global steps_done\n",
    "    sample = random.random()\n",
    "    eps_threshold = EPS_END + (EPS_START - EPS_END) * math.exp(-1. * steps_done / EPS_DECAY)\n",
    "    steps_done += 1\n",
    "    if sample > eps_threshold:\n",
    "        return model(Variable(state.type(dtype), volatile=True)).data.max(1)[1].cpu()\n",
    "    else:\n",
    "        return torch.LongTensor([[random.randrange(2)]])\n",
    "    \n",
    "\n",
    "episode_durations = []\n",
    "def plot_durations():\n",
    "    plt.figure(1)\n",
    "    plt.clf()\n",
    "    durations_t = torch.Tensor(episode_durations)\n",
    "    plt.plot(durations_t.numpy())\n",
    "    # Take 100 episode averages and plot them too\n",
    "    if len(durations_t) >= 100:\n",
    "        means = durations_t.unfold(0, 100, 1).mean(1).view(-1)\n",
    "        means = torch.cat((torch.zeros(99), means))\n",
    "        plt.plot(means.numpy())\n",
    "    display.clear_output(wait=True)\n",
    "    display.display(plt.gcf())"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Training loop\n",
    "\n",
    "Finally, the code for training our model.\n",
    "\n",
    "At the top you can find an `optimize_model` function that performs a single step of the optimization. It first samples a batch, concatenates all the tensors into a single one, computes $Q(s_t, a_t)$ and $V(s_{t+1}) = \\max_a Q(s_{t+1}, a)$, and combines them into our loss. By defition we set $V(s) = 0$ if $s$ is a terminal state.\n",
    "\n",
    "Below, you can find the main training loop. At the beginning we reset the environment and initialize the `state` variable. Then, we sample an action, execute it, observe the next screen and the reward (always 1), and optimize our model once. When the episode ends (our model fails), we restart the loop."
   ]
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    "last_sync = 0\n",
    "def optimize_model():\n",
    "    global last_sync\n",
    "    if len(memory) < BATCH_SIZE:\n",
    "        return\n",
    "    transitions = memory.sample(BATCH_SIZE)\n",
    "    # Transpose the batch (see http://stackoverflow.com/a/19343/3343043 for detailed explanation).\n",
    "    batch = Transition(*zip(*transitions)) \n",
    "\n",
    "    # Compute a mask of non-final states and concatenate the batch elements\n",
    "    non_final_mask = torch.ByteTensor(tuple(map(lambda s: s is not None, batch.next_state)))\n",
    "    if USE_CUDA:\n",
    "        non_final_mask = non_final_mask.cuda()\n",
    "    # We don't want to backprop through the expected action values and volatile will save us\n",
    "    # on temporarily changing the model parameters' requires_grad to False!\n",
    "    non_final_next_states_t = torch.cat(tuple(s for s in batch.next_state if s is not None)).type(dtype)\n",
    "    non_final_next_states = Variable(non_final_next_states_t, volatile=True)\n",
    "    state_batch = Variable(torch.cat(batch.state))\n",
    "    action_batch = Variable(torch.cat(batch.action))\n",
    "    reward_batch = Variable(torch.cat(batch.reward))\n",
    "\n",
    "    # Compute Q(s_t, a) - the model computes Q(s_t), then we select the columns of actions taken\n",
    "    state_action_values = model(state_batch).gather(1, action_batch)\n",
    "\n",
    "    # Compute V(s_{t+1}) for all next states.\n",
    "    next_state_values = Variable(torch.zeros(BATCH_SIZE))\n",
    "    next_state_values[non_final_mask] = model(non_final_next_states).max(1)[0]\n",
    "    # Now, we don't want to mess up the loss with a volatile flag, so let's clear it.\n",
    "    # After this, we'll just end up with a Variable that has requires_grad=False\n",
    "    next_state_values.volatile = False\n",
    "    # Compute the expected Q values\n",
    "    expected_state_action_values = (next_state_values * GAMMA) + reward_batch\n",
    "\n",
    "    # Compute Huber loss\n",
    "    loss = F.smooth_l1_loss(state_action_values, expected_state_action_values)\n",
    "    \n",
    "    # Optimize the model\n",
    "    optimizer.zero_grad()\n",
    "    loss.backward()\n",
    "    for param in model.parameters():\n",
    "        param.grad.data.clamp_(-1, 1)\n",
    "    optimizer.step()\n",
    "\n",
    "\n",
    "for i_episode in count(1):\n",
    "    # Initialize the environment and state\n",
    "    env.reset()\n",
    "    last_screen = get_screen()\n",
    "    current_screen = get_screen()\n",
    "    state = current_screen - last_screen\n",
    "    for t in count():\n",
    "        # Select and perform an action\n",
    "        action = select_action(state)\n",
    "        _, reward, done, _ = env.step(action[0,0])\n",
    "        reward = torch.Tensor([reward])\n",
    "        \n",
    "        # Observe new state\n",
    "        last_screen = current_screen\n",
    "        current_screen = get_screen()\n",
    "        if not done:\n",
    "            next_state = current_screen - last_screen\n",
    "        else:\n",
    "            next_state = None\n",
    "            \n",
    "        # Store the transition in memory\n",
    "        memory.push(state, action, next_state, reward)\n",
    "        \n",
    "        # Move to the next state\n",
    "        state = next_state\n",
    "        \n",
    "        # Perform one step of the optimization (on the target network)\n",
    "        optimize_model()\n",
    "            \n",
    "        if done:\n",
    "            episode_durations.append(t+1)\n",
    "            plot_durations()\n",
    "            break"
   ]
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