##### Copyright 2023 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.
```

25.9

## 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/python3.9/site-packages/tf_agents/replay_buffers/tf_uniform_replay_buffer.py:342: CounterV2 (from tensorflow.python.data.experimental.ops.counter) is deprecated and will be removed in a future version. Instructions for updating: Use `tf.data.Dataset.counter(...)` instead. 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: 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/python3.9/site-packages/tensorflow/python/util/dispatch.py:1176: 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 = 3.154877185821533 step = 400: loss = 2.318402051925659 step = 600: loss = 2.0855250358581543 step = 800: loss = 1.8400838375091553 step = 1000: loss = 1.7026054859161377 step = 1000: Average Return = 44.50 step = 1200: loss = 1.3749397993087769 step = 1400: loss = 1.441072702407837 step = 1600: loss = 1.263155460357666 step = 1800: loss = 1.6114393472671509 step = 2000: loss = 1.3772011995315552 step = 2000: Average Return = 167.10 step = 2200: loss = 1.4033300876617432 step = 2400: loss = 1.1835417747497559 step = 2600: loss = 1.2769452333450317 step = 2800: loss = 1.071426272392273 step = 3000: loss = 1.1817234754562378 step = 3000: Average Return = 329.40 step = 3200: loss = 1.2319562435150146 step = 3400: loss = 1.1435267925262451 step = 3600: loss = 1.2068126201629639 step = 3800: loss = 0.8845781087875366 step = 4000: loss = 0.8474105000495911 step = 4000: Average Return = 316.90 step = 4200: loss = 0.9528285264968872 step = 4400: loss = 0.8406723737716675 step = 4600: loss = 0.8969569206237793 step = 4800: loss = 0.6190842390060425 step = 5000: loss = 0.9327055215835571 step = 5000: Average Return = 283.50 step = 5200: loss = 0.8976035714149475 step = 5400: loss = 0.6578273773193359 step = 5600: loss = 0.8965086936950684 step = 5800: loss = 0.7214109897613525 step = 6000: loss = 0.5149303078651428 step = 6000: Average Return = 276.90 step = 6200: loss = 0.6990393996238708 step = 6400: loss = 0.7126260995864868 step = 6600: loss = 0.6588748693466187 step = 6800: loss = 0.667340874671936 step = 7000: loss = 0.5206128358840942 step = 7000: Average Return = 214.30 step = 7200: loss = 0.809759259223938 step = 7400: loss = 0.8062793016433716 step = 7600: loss = 0.6141629815101624 step = 7800: loss = 0.5564637780189514 step = 8000: loss = 0.6750544309616089 step = 8000: Average Return = 306.20 step = 8200: loss = 0.5368377566337585 step = 8400: loss = 0.5962656736373901 step = 8600: loss = 0.6482559442520142 step = 8800: loss = 0.5133079886436462 step = 9000: loss = 0.38215214014053345 step = 9000: Average Return = 395.20 step = 9200: loss = 0.5137521624565125 step = 9400: loss = 0.503632664680481 step = 9600: loss = 0.4103822112083435 step = 9800: loss = 0.6292715072631836 step = 10000: loss = 0.5354061126708984 step = 10000: Average Return = 471.90 step = 10200: loss = 0.513535737991333 step = 10400: loss = 0.5149332284927368 step = 10600: loss = 0.3598198890686035 step = 10800: loss = 0.38908517360687256 step = 11000: loss = 0.34592729806900024 step = 11000: Average Return = 406.40 step = 11200: loss = 0.507396936416626 step = 11400: loss = 0.5049649477005005 step = 11600: loss = 0.4891279637813568 step = 11800: loss = 0.2773275077342987 step = 12000: loss = 0.30614811182022095 step = 12000: Average Return = 343.40 step = 12200: loss = 0.5184856057167053 step = 12400: loss = 0.36431998014450073 step = 12600: loss = 0.4480145573616028 step = 12800: loss = 0.42815089225769043 step = 13000: loss = 0.4231589436531067 step = 13000: Average Return = 250.30 step = 13200: loss = 0.4650877118110657 step = 13400: loss = 0.287574827671051 step = 13600: loss = 0.45320236682891846 step = 13800: loss = 0.3005008399486542 step = 14000: loss = 0.40336981415748596 step = 14000: Average Return = 210.40 step = 14200: loss = 0.28574761748313904 step = 14400: loss = 0.37719887495040894 step = 14600: loss = 0.3515215516090393 step = 14800: loss = 0.4186158776283264 step = 15000: loss = 0.372530460357666 step = 15000: Average Return = 394.50

## 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)
```

(-14.039999294281007, 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. [swscaler @ 0x55b880007880] 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).