```
In [1]:
```%matplotlib inline

**Author**: `Adam Paszke <https://github.com/apaszke>`

_

This tutorial shows how to use PyTorch to train a Deep Q Learning (DQN) agent
on the CartPole-v0 task from the `OpenAI Gym <https://gym.openai.com/>`

__.

**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 <https://gym.openai.com/envs/CartPole-v0>`

__.

.. 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 <https://gym.openai.com/docs>`

__ 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 <https://github.com/pytorch/vision>`

__).

```
In [2]:
```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

```
```

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.

```
In [3]:
```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)

Now, let's define our model. But first, let quickly recap what a DQN is.

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 <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:

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.

```
In [4]:
```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))

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.

```
In [5]:
```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()

```
```

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.

```
In [6]:
```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())

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.

```
In [ ]:
```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()

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.

```
In [ ]:
```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

```
In [ ]:
```