# DQN C51/Rainbow

## Introduction

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

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: 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()

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.

25.1


## 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

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/python3.9/site-packages/tensorflow/python/autograph/impl/api.py:377: ReplayBuffer.get_next (from tf_agents.replay_buffers.replay_buffer) is deprecated and will be removed in a future version.
Instructions for updating:


## 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/python3.9/site-packages/tensorflow/python/util/dispatch.py:1082: 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:
results = tf.foldr(fn, elems, back_prop=False)
Use:
step = 200: loss = 3.1652722358703613
step = 400: loss = 2.3220953941345215
step = 600: loss = 1.9085898399353027
step = 800: loss = 1.5957838296890259
step = 1000: loss = 1.373847484588623
step = 1000: Average Return = 466.70
step = 1200: loss = 1.2249349355697632
step = 1400: loss = 1.2289665937423706
step = 1600: loss = 1.225049614906311
step = 1800: loss = 1.4009439945220947
step = 2000: loss = 0.8110367059707642
step = 2000: Average Return = 310.30
step = 2200: loss = 0.8426725268363953
step = 2400: loss = 0.9993857145309448
step = 2600: loss = 0.7408146858215332
step = 2800: loss = 1.0472800731658936
step = 3000: loss = 0.8934259414672852
step = 3000: Average Return = 294.80
step = 3200: loss = 0.67853844165802
step = 3400: loss = 0.9168663024902344
step = 3600: loss = 0.6471030712127686
step = 3800: loss = 0.8118085861206055
step = 4000: loss = 0.7178002595901489
step = 4000: Average Return = 339.10
step = 4200: loss = 0.5277565717697144
step = 4400: loss = 0.6562362909317017
step = 4600: loss = 0.6893218755722046
step = 4800: loss = 0.6171445846557617
step = 5000: loss = 0.6233919262886047
step = 5000: Average Return = 192.00
step = 5200: loss = 0.5258955359458923
step = 5400: loss = 0.6037764549255371
step = 5600: loss = 0.6617163419723511
step = 5800: loss = 0.45471426844596863
step = 6000: loss = 0.5623942017555237
step = 6000: Average Return = 375.00
step = 6200: loss = 0.5260623097419739
step = 6400: loss = 0.5474383234977722
step = 6600: loss = 0.6723802089691162
step = 6800: loss = 0.4168206453323364
step = 7000: loss = 0.6093295812606812
step = 7000: Average Return = 396.20
step = 7200: loss = 0.5631401538848877
step = 7400: loss = 0.5302916765213013
step = 7600: loss = 0.4411312937736511
step = 7800: loss = 0.5489145517349243
step = 8000: loss = 0.4881543517112732
step = 8000: Average Return = 352.20
step = 8200: loss = 0.5519999265670776
step = 8400: loss = 0.4684922993183136
step = 8600: loss = 0.523332953453064
step = 8800: loss = 0.4230990409851074
step = 9000: loss = 0.5511386394500732
step = 9000: Average Return = 169.30
step = 9200: loss = 0.5994375944137573
step = 9400: loss = 0.3859468698501587
step = 9600: loss = 0.3768221437931061
step = 9800: loss = 0.3608618378639221
step = 10000: loss = 0.45109525322914124
step = 10000: Average Return = 159.40
step = 10200: loss = 0.4834355115890503
step = 10400: loss = 0.3417738378047943
step = 10600: loss = 0.42035162448883057
step = 10800: loss = 0.513039231300354
step = 11000: loss = 0.4203823208808899
step = 11000: Average Return = 329.90
step = 11200: loss = 0.532701849937439
step = 11400: loss = 0.34555840492248535
step = 11600: loss = 0.23318243026733398
step = 11800: loss = 0.373273640871048
step = 12000: loss = 0.4745432734489441
step = 12000: Average Return = 484.00
step = 12200: loss = 0.38893377780914307
step = 12400: loss = 0.45256471633911133
step = 12600: loss = 0.2996901571750641
step = 12800: loss = 0.44166380167007446
step = 13000: loss = 0.34164178371429443
step = 13000: Average Return = 329.70
step = 13200: loss = 0.45920413732528687
step = 13400: loss = 0.4424200654029846
step = 13600: loss = 0.48878079652786255
step = 13800: loss = 0.48222893476486206
step = 14000: loss = 0.3798040747642517
step = 14000: Average Return = 433.20
step = 14200: loss = 0.46709728240966797
step = 14400: loss = 0.24153408408164978
step = 14600: loss = 0.28913378715515137
step = 14800: loss = 0.36507582664489746
step = 15000: loss = 0.32009801268577576
step = 15000: Average Return = 141.00


## 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)

(-14.11999959945679, 550.0) ### 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."""
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 @ 0x56191e3c7880] 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).

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