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 install -y xvfb ffmpeg
pip install -q 'gym==0.10.11'
pip install -q 'imageio==2.4.0'
pip install -q PILLOW
pip install -q 'pyglet==1.3.2'
pip install -q pyvirtualdisplay
pip install -q tf-agents



ffmpeg is already the newest version (7:3.4.6-0ubuntu0.18.04.1).
xvfb is already the newest version (2:1.19.6-1ubuntu4.4).
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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

tf.compat.v1.enable_v2_behavior()


# 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.compat.v2.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.
21.7

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)

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/python3.6/site-packages/tf_agents/utils/value_ops.py:89: 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 = 3.182137966156006
step = 400: loss = 2.4210848808288574
step = 600: loss = 2.340242862701416
step = 800: loss = 2.0580921173095703
step = 1000: loss = 2.0613021850585938
step = 1000: Average Return = 64.10
step = 1200: loss = 1.77047598361969
step = 1400: loss = 1.7595624923706055
step = 1600: loss = 1.4918586015701294
step = 1800: loss = 1.4464423656463623
step = 2000: loss = 1.3009577989578247
step = 2000: Average Return = 191.40
step = 2200: loss = 1.1830384731292725
step = 2400: loss = 1.0944324731826782
step = 2600: loss = 1.063154935836792
step = 2800: loss = 1.0793070793151855
step = 3000: loss = 1.1424846649169922
step = 3000: Average Return = 247.70
step = 3200: loss = 1.0833452939987183
step = 3400: loss = 0.8716909885406494
step = 3600: loss = 0.908092200756073
step = 3800: loss = 0.8115482330322266
step = 4000: loss = 0.7303909063339233
step = 4000: Average Return = 252.70
step = 4200: loss = 1.0570764541625977
step = 4400: loss = 0.6648094654083252
step = 4600: loss = 0.9327201247215271
step = 4800: loss = 0.6714086532592773
step = 5000: loss = 0.7134998440742493
step = 5000: Average Return = 154.00
step = 5200: loss = 0.6079519391059875
step = 5400: loss = 0.5676228404045105
step = 5600: loss = 0.712378203868866
step = 5800: loss = 0.4793894588947296
step = 6000: loss = 0.8469478487968445
step = 6000: Average Return = 295.90
step = 6200: loss = 0.7207090854644775
step = 6400: loss = 0.5034468173980713
step = 6600: loss = 0.5241268277168274
step = 6800: loss = 0.6233192682266235
step = 7000: loss = 0.6658157706260681
step = 7000: Average Return = 458.40
step = 7200: loss = 0.48315566778182983
step = 7400: loss = 0.5506547689437866
step = 7600: loss = 0.36968711018562317
step = 7800: loss = 0.35069745779037476
step = 8000: loss = 0.3564116656780243
step = 8000: Average Return = 418.00
step = 8200: loss = 0.4515156149864197
step = 8400: loss = 0.35601940751075745
step = 8600: loss = 0.45192813873291016
step = 8800: loss = 0.3597773313522339
step = 9000: loss = 0.5478107929229736
step = 9000: Average Return = 353.90
step = 9200: loss = 0.5436872839927673
step = 9400: loss = 0.42222124338150024
step = 9600: loss = 0.5436835289001465
step = 9800: loss = 0.3003008961677551
step = 10000: loss = 0.23883846402168274
step = 10000: Average Return = 386.80
step = 10200: loss = 0.32303956151008606
step = 10400: loss = 0.34102070331573486
step = 10600: loss = 0.3647277355194092
step = 10800: loss = 0.4080239534378052
step = 11000: loss = 0.4575228989124298
step = 11000: Average Return = 375.60
step = 11200: loss = 0.5556718111038208
step = 11400: loss = 0.4088587760925293
step = 11600: loss = 0.3414197266101837
step = 11800: loss = 0.5044705271720886
step = 12000: loss = 0.34521108865737915
step = 12000: Average Return = 281.30
step = 12200: loss = 0.35382676124572754
step = 12400: loss = 0.5887238383293152
step = 12600: loss = 0.2820581793785095
step = 12800: loss = 0.4514696002006531
step = 13000: loss = 0.4163169860839844
step = 13000: Average Return = 343.60
step = 13200: loss = 0.3318667411804199
step = 13400: loss = 0.3408347964286804
step = 13600: loss = 0.35240083932876587
step = 13800: loss = 0.2687753438949585
step = 14000: loss = 0.2804262340068817
step = 14000: Average Return = 457.90
step = 14200: loss = 0.21197451651096344
step = 14400: loss = 0.40651118755340576
step = 14600: loss = 0.35050544142723083
step = 14800: loss = 0.2924571633338928
step = 15000: loss = 0.32729238271713257
step = 15000: Average Return = 394.10

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)
(-13.784999895095826, 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.

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).