##### Copyright 2018 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 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). 0 upgraded, 0 newly installed, 0 to remove and 108 not upgraded.

```
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:

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)

### 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).