Reinforcement Learning (DQN) tutorial
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Author: Adam Paszke
This tutorial shows how to use PyTorch to train a Deep Q Learning (DQN) agent on the CartPole-v0 task from the OpenAI Gym.
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.
As the agent observes the current state of the environment and chooses an action, the environmenttransitions 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 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).
import gymimport mathimport randomimport numpy as npimport matplotlibimport matplotlib.pyplot as pltfrom collections import namedtuplefrom itertools import countfrom copy import deepcopyfrom PIL import Imageimport torchimport torch.nn as nnimport torch.optim as optimimport torch.autograd as autogradimport torch.nn.functional as Fimport torchvision.transforms as Tenv = gym.make('CartPole-v0')is_ipython = 'inline' in matplotlib.get_backend()if is_ipython: from IPython import display
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 environmentReplayMemory
- 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.
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.
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
The main idea behind Q-learning is that if we had a function
However, we don’t know everything about the world, so we don’t have access to
For our training update rule, we’ll use a fact that every
The difference between the two sides of the equality is known as the temporal difference error,
To minimise this error, we will use the 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-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
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.
resize = T.Compose([T.ToPILImage(), T.Scale(40, interpolation=Image.CUBIC), T.ToTensor()])# This is based on the code from gym.screen_width = 600def 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 CARTdef 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()
Training
Hyperparameters and utilities
This cell instantiates our model and its optimizer, and defines some utilities:
Variable
- this is a simple wrapper aroundtorch.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 atEPS_START
and will decay exponentially towardsEPS_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.
BATCH_SIZE = 128GAMMA = 0.999EPS_START = 0.9EPS_END = 0.05EPS_DECAY = 200USE_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 = 0def 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())
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
last_sync = 0def 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.
num_episodes = 10for i_episode in range(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
Total running time of the script: ( 0 minutes 0.000 seconds)
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