##### Copyright 2021 The TF-Agents Authors.

View on TensorFlow.org | Run in Google Colab | View source on GitHub | Download notebook |

## 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)
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:

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.
```

14.3

## 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/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: 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: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: 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 = 3.18833065032959 step = 400: loss = 2.0754148960113525 step = 600: loss = 1.6196262836456299 step = 800: loss = 1.6139719486236572 step = 1000: loss = 1.6449038982391357 step = 1000: Average Return = 69.50 step = 1200: loss = 1.442345142364502 step = 1400: loss = 1.3810657262802124 step = 1600: loss = 1.439863920211792 step = 1800: loss = 1.250838041305542 step = 2000: loss = 0.9620616436004639 step = 2000: Average Return = 111.20 step = 2200: loss = 0.9732844829559326 step = 2400: loss = 1.1604586839675903 step = 2600: loss = 1.0683619976043701 step = 2800: loss = 0.7791318297386169 step = 3000: loss = 0.8672434091567993 step = 3000: Average Return = 121.80 step = 3200: loss = 0.8914871215820312 step = 3400: loss = 0.7287296056747437 step = 3600: loss = 0.7770305275917053 step = 3800: loss = 0.8099956512451172 step = 4000: loss = 0.7211952209472656 step = 4000: Average Return = 124.00 step = 4200: loss = 0.7737867832183838 step = 4400: loss = 0.37551194429397583 step = 4600: loss = 0.9274032115936279 step = 4800: loss = 0.7041550278663635 step = 5000: loss = 0.7585321664810181 step = 5000: Average Return = 122.10 step = 5200: loss = 0.7196154594421387 step = 5400: loss = 0.5071319341659546 step = 5600: loss = 0.6105386018753052 step = 5800: loss = 0.9854182004928589 step = 6000: loss = 0.8031271696090698 step = 6000: Average Return = 119.30 step = 6200: loss = 0.5764856338500977 step = 6400: loss = 0.6573711633682251 step = 6600: loss = 0.5899996757507324 step = 6800: loss = 0.7075515985488892 step = 7000: loss = 0.6315189003944397 step = 7000: Average Return = 148.80 step = 7200: loss = 0.613953173160553 step = 7400: loss = 0.5542221069335938 step = 7600: loss = 0.6412272453308105 step = 7800: loss = 0.659490704536438 step = 8000: loss = 0.7146942019462585 step = 8000: Average Return = 323.60 step = 8200: loss = 0.745093584060669 step = 8400: loss = 0.6035239696502686 step = 8600: loss = 0.5051594972610474 step = 8800: loss = 0.4333418905735016 step = 9000: loss = 0.41490358114242554 step = 9000: Average Return = 171.40 step = 9200: loss = 0.5744825005531311 step = 9400: loss = 0.3952058255672455 step = 9600: loss = 0.4711418151855469 step = 9800: loss = 0.3695340156555176 step = 10000: loss = 0.4991128444671631 step = 10000: Average Return = 239.10 step = 10200: loss = 0.3210873305797577 step = 10400: loss = 0.44588786363601685 step = 10600: loss = 0.46316105127334595 step = 10800: loss = 0.4235161542892456 step = 11000: loss = 0.3815745711326599 step = 11000: Average Return = 262.00 step = 11200: loss = 0.24434217810630798 step = 11400: loss = 0.4426969289779663 step = 11600: loss = 0.6227148771286011 step = 11800: loss = 0.6028870344161987 step = 12000: loss = 0.32088762521743774 step = 12000: Average Return = 238.40 step = 12200: loss = 0.26182225346565247 step = 12400: loss = 0.430329829454422 step = 12600: loss = 0.4523652195930481 step = 12800: loss = 0.42841729521751404 step = 13000: loss = 0.37387534976005554 step = 13000: Average Return = 280.50 step = 13200: loss = 0.339707612991333 step = 13400: loss = 0.3781306743621826 step = 13600: loss = 0.5201965570449829 step = 13800: loss = 0.20747043192386627 step = 14000: loss = 0.4218123257160187 step = 14000: Average Return = 296.00 step = 14200: loss = 0.27447056770324707 step = 14400: loss = 0.2909761965274811 step = 14600: loss = 0.5002873539924622 step = 14800: loss = 0.4098619818687439 step = 15000: loss = 0.272499680519104 step = 15000: Average Return = 184.50

## 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)
```

(56.79499969482422, 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."""
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. /tmpfs/src/tf_docs_env/lib/python3.7/site-packages/imageio/plugins/ffmpeg.py:727: DeprecationWarning: tostring() is deprecated. Use tobytes() instead. self._proc.stdin.write(im.tostring()) [swscaler @ 0x560d6a15e3c0] 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).