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DQN C51/Rainbow

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Introduction

This example shows how to train a Categorical DQN (C51) agent on the Cartpole environment using the TF-Agents library.

Cartpole environment

Make sure you take a look through the DQN tutorial as a prerequisite. This tutorial will assume familiarity with the DQN tutorial; it will mainly focus on the differences between DQN and C51.

Setup

If you haven't installed tf-agents yet, run:

sudo apt-get update
sudo apt-get install -y xvfb ffmpeg freeglut3-dev
pip install 'imageio==2.4.0'
pip install pyvirtualdisplay
pip install tf-agents
pip install pyglet
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function

import base64
import imageio
import IPython
import matplotlib
import matplotlib.pyplot as plt
import PIL.Image
import pyvirtualdisplay

import tensorflow as tf

from tf_agents.agents.categorical_dqn import categorical_dqn_agent
from tf_agents.drivers import dynamic_step_driver
from tf_agents.environments import suite_gym
from tf_agents.environments import tf_py_environment
from tf_agents.eval import metric_utils
from tf_agents.metrics import tf_metrics
from tf_agents.networks import categorical_q_network
from tf_agents.policies import random_tf_policy
from tf_agents.replay_buffers import tf_uniform_replay_buffer
from tf_agents.trajectories import trajectory
from tf_agents.utils import common

# Set up a virtual display for rendering OpenAI gym environments.
display = pyvirtualdisplay.Display(visible=0, size=(1400, 900)).start()

Hyperparameters

env_name = "CartPole-v1" # @param {type:"string"}
num_iterations = 15000 # @param {type:"integer"}

initial_collect_steps = 1000  # @param {type:"integer"} 
collect_steps_per_iteration = 1  # @param {type:"integer"}
replay_buffer_capacity = 100000  # @param {type:"integer"}

fc_layer_params = (100,)

batch_size = 64  # @param {type:"integer"}
learning_rate = 1e-3  # @param {type:"number"}
gamma = 0.99
log_interval = 200  # @param {type:"integer"}

num_atoms = 51  # @param {type:"integer"}
min_q_value = -20  # @param {type:"integer"}
max_q_value = 20  # @param {type:"integer"}
n_step_update = 2  # @param {type:"integer"}

num_eval_episodes = 10  # @param {type:"integer"}
eval_interval = 1000  # @param {type:"integer"}

Environment

Load the environment as before, with one for training and one for evaluation. Here we use CartPole-v1 (vs. CartPole-v0 in the DQN tutorial), which has a larger max reward of 500 rather than 200.

train_py_env = suite_gym.load(env_name)
eval_py_env = suite_gym.load(env_name)

train_env = tf_py_environment.TFPyEnvironment(train_py_env)
eval_env = tf_py_environment.TFPyEnvironment(eval_py_env)

Agent

C51 is a Q-learning algorithm based on DQN. Like DQN, it can be used on any environment with a discrete action space.

The main difference between C51 and DQN is that rather than simply predicting the Q-value for each state-action pair, C51 predicts a histogram model for the probability distribution of the Q-value:

Example C51 Distribution

By learning the distribution rather than simply the expected value, the algorithm is able to stay more stable during training, leading to improved final performance. This is particularly true in situations with bimodal or even multimodal value distributions, where a single average does not provide an accurate picture.

In order to train on probability distributions rather than on values, C51 must perform some complex distributional computations in order to calculate its loss function. But don't worry, all of this is taken care of for you in TF-Agents!

To create a C51 Agent, we first need to create a CategoricalQNetwork. The API of the CategoricalQNetwork is the same as that of the QNetwork, except that there is an additional argument num_atoms. This represents the number of support points in our probability distribution estimates. (The above image includes 10 support points, each represented by a vertical blue bar.) As you can tell from the name, the default number of atoms is 51.

categorical_q_net = categorical_q_network.CategoricalQNetwork(
    train_env.observation_spec(),
    train_env.action_spec(),
    num_atoms=num_atoms,
    fc_layer_params=fc_layer_params)

We also need an optimizer to train the network we just created, and a train_step_counter variable to keep track of how many times the network was updated.

Note that one other significant difference from vanilla DqnAgent is that we now need to specify min_q_value and max_q_value as arguments. These specify the most extreme values of the support (in other words, the most extreme of the 51 atoms on either side). Make sure to choose these appropriately for your particular environment. Here we use -20 and 20.

optimizer = tf.compat.v1.train.AdamOptimizer(learning_rate=learning_rate)

train_step_counter = tf.Variable(0)

agent = categorical_dqn_agent.CategoricalDqnAgent(
    train_env.time_step_spec(),
    train_env.action_spec(),
    categorical_q_network=categorical_q_net,
    optimizer=optimizer,
    min_q_value=min_q_value,
    max_q_value=max_q_value,
    n_step_update=n_step_update,
    td_errors_loss_fn=common.element_wise_squared_loss,
    gamma=gamma,
    train_step_counter=train_step_counter)
agent.initialize()

One last thing to note is that we also added an argument to use n-step updates with \(n\) = 2. In single-step Q-learning (\(n\) = 1), we only compute the error between the Q-values at the current time step and the next time step using the single-step return (based on the Bellman optimality equation). The single-step return is defined as:

\(G_t = R_{t + 1} + \gamma V(s_{t + 1})\)

where we define \(V(s) = \max_a{Q(s, a)}\).

N-step updates involve expanding the standard single-step return function \(n\) times:

\(G_t^n = R_{t + 1} + \gamma R_{t + 2} + \gamma^2 R_{t + 3} + \dots + \gamma^n V(s_{t + n})\)

N-step updates enable the agent to bootstrap from further in the future, and with the right value of \(n\), this often leads to faster learning.

Although C51 and n-step updates are often combined with prioritized replay to form the core of the Rainbow agent, we saw no measurable improvement from implementing prioritized replay. Moreover, we find that when combining our C51 agent with n-step updates alone, our agent performs as well as other Rainbow agents on the sample of Atari environments we've tested.

Metrics and Evaluation

The most common metric used to evaluate a policy is the average return. The return is the sum of rewards obtained while running a policy in an environment for an episode, and we usually average this over a few episodes. We can compute the average return metric as follows.

def compute_avg_return(environment, policy, num_episodes=10):

  total_return = 0.0
  for _ in range(num_episodes):

    time_step = environment.reset()
    episode_return = 0.0

    while not time_step.is_last():
      action_step = policy.action(time_step)
      time_step = environment.step(action_step.action)
      episode_return += time_step.reward
    total_return += episode_return

  avg_return = total_return / num_episodes
  return avg_return.numpy()[0]


random_policy = random_tf_policy.RandomTFPolicy(train_env.time_step_spec(),
                                                train_env.action_spec())

compute_avg_return(eval_env, random_policy, num_eval_episodes)

# Please also see the metrics module for standard implementations of different
# metrics.
20.0

Data Collection

As in the DQN tutorial, set up the replay buffer and the initial data collection with the random policy.

replay_buffer = tf_uniform_replay_buffer.TFUniformReplayBuffer(
    data_spec=agent.collect_data_spec,
    batch_size=train_env.batch_size,
    max_length=replay_buffer_capacity)

def collect_step(environment, policy):
  time_step = environment.current_time_step()
  action_step = policy.action(time_step)
  next_time_step = environment.step(action_step.action)
  traj = trajectory.from_transition(time_step, action_step, next_time_step)

  # Add trajectory to the replay buffer
  replay_buffer.add_batch(traj)

for _ in range(initial_collect_steps):
  collect_step(train_env, random_policy)

# This loop is so common in RL, that we provide standard implementations of
# these. For more details see the drivers module.

# Dataset generates trajectories with shape [BxTx...] where
# T = n_step_update + 1.
dataset = replay_buffer.as_dataset(
    num_parallel_calls=3, sample_batch_size=batch_size,
    num_steps=n_step_update + 1).prefetch(3)

iterator = iter(dataset)
WARNING:tensorflow:From /tmpfs/src/tf_docs_env/lib/python3.7/site-packages/tensorflow/python/data/experimental/ops/counter.py:66: scan (from tensorflow.python.data.experimental.ops.scan_ops) is deprecated and will be removed in a future version.
Instructions for updating:
Use `tf.data.Dataset.scan(...) instead
WARNING:tensorflow:From /tmpfs/src/tf_docs_env/lib/python3.7/site-packages/tensorflow/python/autograph/impl/api.py:382: ReplayBuffer.get_next (from tf_agents.replay_buffers.replay_buffer) is deprecated and will be removed in a future version.
Instructions for updating:
Use `as_dataset(..., single_deterministic_pass=False) instead.

Training the agent

The training loop involves both collecting data from the environment and optimizing the agent's networks. Along the way, we will occasionally evaluate the agent's policy to see how we are doing.

The following will take ~7 minutes to run.

try:
  %%time
except:
  pass

# (Optional) Optimize by wrapping some of the code in a graph using TF function.
agent.train = common.function(agent.train)

# Reset the train step
agent.train_step_counter.assign(0)

# Evaluate the agent's policy once before training.
avg_return = compute_avg_return(eval_env, agent.policy, num_eval_episodes)
returns = [avg_return]

for _ in range(num_iterations):

  # Collect a few steps using collect_policy and save to the replay buffer.
  for _ in range(collect_steps_per_iteration):
    collect_step(train_env, agent.collect_policy)

  # Sample a batch of data from the buffer and update the agent's network.
  experience, unused_info = next(iterator)
  train_loss = agent.train(experience)

  step = agent.train_step_counter.numpy()

  if step % log_interval == 0:
    print('step = {0}: loss = {1}'.format(step, train_loss.loss))

  if step % eval_interval == 0:
    avg_return = compute_avg_return(eval_env, agent.policy, num_eval_episodes)
    print('step = {0}: Average Return = {1:.2f}'.format(step, avg_return))
    returns.append(avg_return)
WARNING:tensorflow:From /tmpfs/src/tf_docs_env/lib/python3.7/site-packages/tensorflow/python/util/dispatch.py:206: calling foldr_v2 (from tensorflow.python.ops.functional_ops) with back_prop=False is deprecated and will be removed in a future version.
Instructions for updating:
back_prop=False is deprecated. Consider using tf.stop_gradient instead.
Instead of:
results = tf.foldr(fn, elems, back_prop=False)
Use:
results = tf.nest.map_structure(tf.stop_gradient, tf.foldr(fn, elems))
step = 200: loss = 3.199000597000122
step = 400: loss = 2.083357810974121
step = 600: loss = 1.9901162385940552
step = 800: loss = 1.9055049419403076
step = 1000: loss = 1.7382612228393555
step = 1000: Average Return = 34.40
step = 1200: loss = 1.3624987602233887
step = 1400: loss = 1.548039197921753
step = 1600: loss = 1.4193217754364014
step = 1800: loss = 1.3339967727661133
step = 2000: loss = 1.1471226215362549
step = 2000: Average Return = 91.10
step = 2200: loss = 1.360352873802185
step = 2400: loss = 1.4253160953521729
step = 2600: loss = 0.9550995826721191
step = 2800: loss = 0.9822611808776855
step = 3000: loss = 1.0512573719024658
step = 3000: Average Return = 102.60
step = 3200: loss = 1.131516456604004
step = 3400: loss = 1.0834283828735352
step = 3600: loss = 0.8771724104881287
step = 3800: loss = 0.7854692935943604
step = 4000: loss = 0.7451740503311157
step = 4000: Average Return = 179.10
step = 4200: loss = 0.6963338851928711
step = 4400: loss = 0.8579068183898926
step = 4600: loss = 0.735978364944458
step = 4800: loss = 0.5723521709442139
step = 5000: loss = 0.6422518491744995
step = 5000: Average Return = 138.00
step = 5200: loss = 0.5242955684661865
step = 5400: loss = 0.869032621383667
step = 5600: loss = 0.7798122763633728
step = 5800: loss = 0.745892345905304
step = 6000: loss = 0.7540864944458008
step = 6000: Average Return = 155.80
step = 6200: loss = 0.6851651668548584
step = 6400: loss = 0.7417727112770081
step = 6600: loss = 0.7385923862457275
step = 6800: loss = 0.8823254108428955
step = 7000: loss = 0.6216408014297485
step = 7000: Average Return = 146.90
step = 7200: loss = 0.3905255198478699
step = 7400: loss = 0.5030156373977661
step = 7600: loss = 0.6326021552085876
step = 7800: loss = 0.6071780920028687
step = 8000: loss = 0.49069637060165405
step = 8000: Average Return = 332.70
step = 8200: loss = 0.7194125056266785
step = 8400: loss = 0.7707428932189941
step = 8600: loss = 0.42258384823799133
step = 8800: loss = 0.5215793251991272
step = 9000: loss = 0.6949542164802551
step = 9000: Average Return = 174.10
step = 9200: loss = 0.7312793731689453
step = 9400: loss = 0.5663323402404785
step = 9600: loss = 0.8518731594085693
step = 9800: loss = 0.5256152153015137
step = 10000: loss = 0.578148603439331
step = 10000: Average Return = 147.40
step = 10200: loss = 0.46965712308883667
step = 10400: loss = 0.5685954093933105
step = 10600: loss = 0.5819060802459717
step = 10800: loss = 0.792033851146698
step = 11000: loss = 0.5804982781410217
step = 11000: Average Return = 186.80
step = 11200: loss = 0.4973406195640564
step = 11400: loss = 0.33229681849479675
step = 11600: loss = 0.5267124176025391
step = 11800: loss = 0.585414469242096
step = 12000: loss = 0.6697092652320862
step = 12000: Average Return = 135.30
step = 12200: loss = 0.30732017755508423
step = 12400: loss = 0.490392804145813
step = 12600: loss = 0.28014713525772095
step = 12800: loss = 0.456543892621994
step = 13000: loss = 0.48237597942352295
step = 13000: Average Return = 182.70
step = 13200: loss = 0.5447070598602295
step = 13400: loss = 0.4602382481098175
step = 13600: loss = 0.5659506320953369
step = 13800: loss = 0.47906267642974854
step = 14000: loss = 0.4060840904712677
step = 14000: Average Return = 153.00
step = 14200: loss = 0.6457054018974304
step = 14400: loss = 0.4795544147491455
step = 14600: loss = 0.16895757615566254
step = 14800: loss = 0.5005109906196594
step = 15000: loss = 0.5339224338531494
step = 15000: Average Return = 165.10

Visualization

Plots

We can plot return vs global steps to see the performance of our agent. In Cartpole-v1, the environment gives a reward of +1 for every time step the pole stays up, and since the maximum number of steps is 500, the maximum possible return is also 500.

steps = range(0, num_iterations + 1, eval_interval)
plt.plot(steps, returns)
plt.ylabel('Average Return')
plt.xlabel('Step')
plt.ylim(top=550)
(19.485000991821288, 550.0)

png

Videos

It is helpful to visualize the performance of an agent by rendering the environment at each step. Before we do that, let us first create a function to embed videos in this colab.

def embed_mp4(filename):
  """Embeds an mp4 file in the notebook."""
  video = open(filename,'rb').read()
  b64 = base64.b64encode(video)
  tag = '''
  <video width="640" height="480" controls>
    <source src="data:video/mp4;base64,{0}" type="video/mp4">
  Your browser does not support the video tag.
  </video>'''.format(b64.decode())

  return IPython.display.HTML(tag)

The following code visualizes the agent's policy for a few episodes:

num_episodes = 3
video_filename = 'imageio.mp4'
with imageio.get_writer(video_filename, fps=60) as video:
  for _ in range(num_episodes):
    time_step = eval_env.reset()
    video.append_data(eval_py_env.render())
    while not time_step.is_last():
      action_step = agent.policy.action(time_step)
      time_step = eval_env.step(action_step.action)
      video.append_data(eval_py_env.render())

embed_mp4(video_filename)
WARNING:root:IMAGEIO FFMPEG_WRITER WARNING: input image is not divisible by macro_block_size=16, resizing from (400, 600) to (400, 608) to ensure video compatibility with most codecs and players. To prevent resizing, make your input image divisible by the macro_block_size or set the macro_block_size to None (risking incompatibility). You may also see a FFMPEG warning concerning speedloss due to data not being aligned.
[swscaler @ 0x5646eec183c0] Warning: data is not aligned! This can lead to a speed loss

C51 tends to do slightly better than DQN on CartPole-v1, but the difference between the two agents becomes more and more significant in increasingly complex environments. For example, on the full Atari 2600 benchmark, C51 demonstrates a mean score improvement of 126% over DQN after normalizing with respect to a random agent. Additional improvements can be gained by including n-step updates.

For a deeper dive into the C51 algorithm, see A Distributional Perspective on Reinforcement Learning (2017).