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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 Reinforcement Learning (DQN) tutorial
Author
Step2:  Replay Memory
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.
For this, we're going to need two classses
Step3:  Now, let's define our model. But first, let quickly recap what a DQN is.
DQN algorithm
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.
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.
The main idea behind Q-learning is that if we had a function
$Q^*
Step4:  Input extraction
^^^^^^^^^^^^^^^^
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.
Step5:  Training
Hyperparameters and utilities
This cell instantiates our model and its optimizer, and defines some
utilities
Step6:  Training loop
Finally, the code for training our model.
Here, 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.
Step7:  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.
Below, num_episodes is set small. You should download
the notebook and run lot more epsiodes.
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Python Code:
import gym
import math
import random
import numpy as np
import matplotlib
import matplotlib.pyplot as plt
from collections import namedtuple
from itertools import count
from copy import deepcopy
from PIL import Image
from __future__ import print_function, division
import torch
import torch.nn as nn
import torch.optim as optim
import torch.autograd as autograd
import torch.nn.functional as F
import torchvision.transforms as T
env = gym.make('CartPole-v0')
env = env.unwrapped
is_ipython = 'inline' in matplotlib.get_backend()
if is_ipython:
    from IPython import display
Explanation: Reinforcement Learning (DQN) tutorial
Author: Adam Paszke &lt;https://github.com/apaszke&gt;_
This tutorial shows how to use PyTorch to train a Deep Q Learning (DQN) agent
on the CartPole-v0 task from the OpenAI Gym &lt;https://gym.openai.com/&gt;__.
Task
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 &lt;https://gym.openai.com/envs/CartPole-v0&gt;__.
.. figure:: /_static/img/cartpole.gif
   :alt: cartpole
cartpole
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.
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.
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.
Packages
First, let's import needed packages. Firstly, we need
gym &lt;https://gym.openai.com/docs&gt;__ for the environment
(Install using pip install gym).
We'll also use the following from PyTorch:
neural networks (torch.nn)
optimization (torch.optim)
automatic differentiation (torch.autograd)
utilities for vision tasks (torchvision - a separate
   package &lt;https://github.com/pytorch/vision&gt;__).
End of explanation
Transition = namedtuple('Transition',
                        ('state', 'action', 'next_state', 'reward'))
class ReplayMemory(object):
    def __init__(self, capacity):
        self.capacity = capacity
        self.memory = []
        self.position = 0
    def push(self, *args):
        Saves a transition.
        if len(self.memory) < self.capacity:
            self.memory.append(None)
        self.memory[self.position] = Transition(*args)
        self.position = (self.position + 1) % self.capacity
    def sample(self, batch_size):
        return random.sample(self.memory, batch_size)
    def __len__(self):
        return len(self.memory)
Explanation: Replay Memory
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.
For this, we're going to need two classses:
Transition - a named tuple representing a single transition in
   our environment
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.
End of explanation
class DQN(nn.Module):
    def __init__(self):
        super(DQN, self).__init__()
        self.conv1 = nn.Conv2d(3, 16, kernel_size=5, stride=2)
        self.bn1 = nn.BatchNorm2d(16)
        self.conv2 = nn.Conv2d(16, 32, kernel_size=5, stride=2)
        self.bn2 = nn.BatchNorm2d(32)
        self.conv3 = nn.Conv2d(32, 32, kernel_size=5, stride=2)
        self.bn3 = nn.BatchNorm2d(32)
        self.head = nn.Linear(448, 2)
    def forward(self, x):
        x = F.relu(self.bn1(self.conv1(x)))
        x = F.relu(self.bn2(self.conv2(x)))
        x = F.relu(self.bn3(self.conv3(x)))
        return self.head(x.view(x.size(0), -1))
Explanation: Now, let's define our model. But first, let quickly recap what a DQN is.
DQN algorithm
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.
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.
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:
\begin{align}\pi^(s) = \arg!\max_a \ Q^(s, a)\end{align}
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
$Q^$.
For our training update rule, we'll use a fact that every $Q$
function for some policy obeys the Bellman equation:
\begin{align}Q^{\pi}(s, a) = r + \gamma Q^{\pi}(s', \pi(s'))\end{align}
The difference between the two sides of the equality is known as the
temporal difference error, $\delta$:
\begin{align}\delta = Q(s, a) - (r + \gamma \max_a Q(s', a))\end{align}
To minimise this error, we will use the Huber
loss &lt;https://en.wikipedia.org/wiki/Huber_loss&gt;__. 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:
\begin{align}\mathcal{L} = \frac{1}{|B|}\sum_{(s, a, s', r) \ \in \ B} \mathcal{L}(\delta)\end{align}
\begin{align}\text{where} \quad \mathcal{L}(\delta) = \begin{cases}
     \frac{1}{2}{\delta^2}  & \text{for } |\delta| \le 1, \
     |\delta| - \frac{1}{2} & \text{otherwise.}
   \end{cases}\end{align}
Q-network
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.
End of explanation
resize = T.Compose([T.ToPILImage(),
                    T.Scale(40, interpolation=Image.CUBIC),
                    T.ToTensor()])
# This is based on the code from gym.
screen_width = 600
def get_cart_location():
    world_width = env.x_threshold * 2
    scale = screen_width / world_width
    return int(env.state[0] * scale + screen_width / 2.0)  # MIDDLE OF CART
def get_screen():
    screen = env.render(mode='rgb_array').transpose(
        (2, 0, 1))  # transpose into torch order (CHW)
    # Strip off the top and bottom of the screen
    screen = screen[:, 160:320]
    view_width = 320
    cart_location = get_cart_location()
    if cart_location < view_width // 2:
        slice_range = slice(view_width)
    elif cart_location > (screen_width - view_width // 2):
        slice_range = slice(-view_width, None)
    else:
        slice_range = slice(cart_location - view_width // 2,
                            cart_location + view_width // 2)
    # Strip off the edges, so that we have a square image centered on a cart
    screen = screen[:, :, slice_range]
    # Convert to float, rescare, convert to torch tensor
    # (this doesn't require a copy)
    screen = np.ascontiguousarray(screen, dtype=np.float32) / 255
    screen = torch.from_numpy(screen)
    # Resize, and add a batch dimension (BCHW)
    return resize(screen).unsqueeze(0)
env.reset()
plt.imshow(get_screen().squeeze(0).permute(1, 2, 0).numpy(), interpolation='none')
plt.show()
Explanation: Input extraction
^^^^^^^^^^^^^^^^
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.
End of explanation
BATCH_SIZE = 128
GAMMA = 0.999
EPS_START = 0.9
EPS_END = 0.05
EPS_DECAY = 200
USE_CUDA = torch.cuda.is_available()
model = DQN()
memory = ReplayMemory(10000)
optimizer = optim.RMSprop(model.parameters())
if USE_CUDA:
    model.cuda()
class Variable(autograd.Variable):
    def __init__(self, data, *args, **kwargs):
        if USE_CUDA:
            data = data.cuda()
        super(Variable, self).__init__(data, *args, **kwargs)
steps_done = 0
def select_action(state):
    global steps_done
    sample = random.random()
    eps_threshold = EPS_END + (EPS_START - EPS_END) * \
        math.exp(-1. * steps_done / EPS_DECAY)
    steps_done += 1
    if sample > eps_threshold:
        return model(Variable(state, volatile=True)).data.max(1)[1].cpu()
    else:
        return torch.LongTensor([[random.randrange(2)]])
episode_durations = []
def plot_durations():
    plt.figure(1)
    plt.clf()
    durations_t = torch.Tensor(episode_durations)
    plt.xlabel('Episode')
    plt.ylabel('Duration')
    plt.plot(durations_t.numpy())
    # Take 100 episode averages and plot them too
    if len(durations_t) >= 100:
        means = durations_t.unfold(0, 100, 1).mean(1).view(-1)
        means = torch.cat((torch.zeros(99), means))
        plt.plot(means.numpy())
    if is_ipython:
        display.clear_output(wait=True)
        display.display(plt.gcf())
Explanation: Training
Hyperparameters and utilities
This cell instantiates our model and its optimizer, and defines some
utilities:
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.
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.
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.
End of explanation
last_sync = 0
def optimize_model():
    global last_sync
    if len(memory) < BATCH_SIZE:
        return
    transitions = memory.sample(BATCH_SIZE)
    # Transpose the batch (see http://stackoverflow.com/a/19343/3343043 for
    # detailed explanation).
    batch = Transition(*zip(*transitions))
    # Compute a mask of non-final states and concatenate the batch elements
    non_final_mask = torch.ByteTensor(
        tuple(map(lambda s: s is not None, batch.next_state)))
    if USE_CUDA:
        non_final_mask = non_final_mask.cuda()
    # We don't want to backprop through the expected action values and volatile
    # will save us on temporarily changing the model parameters'
    # requires_grad to False!
    non_final_next_states = Variable(torch.cat([s for s in batch.next_state
                                                if s is not None]),
                                     volatile=True)
    state_batch = Variable(torch.cat(batch.state))
    action_batch = Variable(torch.cat(batch.action))
    reward_batch = Variable(torch.cat(batch.reward))
    # Compute Q(s_t, a) - the model computes Q(s_t), then we select the
    # columns of actions taken
    state_action_values = model(state_batch).gather(1, action_batch)
    # Compute V(s_{t+1}) for all next states.
    next_state_values = Variable(torch.zeros(BATCH_SIZE))
    next_state_values[non_final_mask] = model(non_final_next_states).max(1)[0]
    # Now, we don't want to mess up the loss with a volatile flag, so let's
    # clear it. After this, we'll just end up with a Variable that has
    # requires_grad=False
    next_state_values.volatile = False
    # Compute the expected Q values
    expected_state_action_values = (next_state_values * GAMMA) + reward_batch
    # Compute Huber loss
    loss = F.smooth_l1_loss(state_action_values, expected_state_action_values)
    # Optimize the model
    optimizer.zero_grad()
    loss.backward()
    for param in model.parameters():
        param.grad.data.clamp_(-1, 1)
    optimizer.step()
Explanation: Training loop
Finally, the code for training our model.
Here, 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.
End of explanation
num_episodes = 10
for i_episode in xrange(num_episodes):
    # Initialize the environment and state
    env.reset()
    last_screen = get_screen()
    current_screen = get_screen()
    state = current_screen - last_screen
    for t in count():
        # Select and perform an action
        action = select_action(state)
        _, reward, done, _ = env.step(action[0, 0])
        reward = torch.Tensor([reward])
        # Observe new state
        last_screen = current_screen
        current_screen = get_screen()
        if not done:
            next_state = current_screen - last_screen
        else:
            next_state = None
        # Store the transition in memory
        memory.push(state, action, next_state, reward)
        # Move to the next state
        state = next_state
        # Perform one step of the optimization (on the target network)
        optimize_model()
        if done:
            episode_durations.append(t + 1)
            plot_durations()
            break
Explanation: 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.
Below, num_episodes is set small. You should download
the notebook and run lot more epsiodes.
End of explanation
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