Exercise TD q-learning with frozenlake from gym API

Introduction
Requirements
- Knowledge
- Prerequisites
Python Modules
Exercise
Literature
Licenses

Introduction

In this notebook you will use Temporal-Difference learning (TD learning), especially the Q-learning algorithm to train the agent for the Frozenlake environment provided by the gym API. The main difference between TD learning and Monte Carlo methods is that instead of learning from whole episodes one goes even one more step back and learns based on a step by step approach.

To get familiar with the Frozenlake environment it is suggested to read through the first part of the notebook exercise-monte-carlo-frozenlake-gym. Also the usage of tie-breaking argmax and policy performance testing is explaned their in more detail.

Requirements

Knowledge

To solve this notebook you should aquire knowledge about Temporal-Difference learning, especially Q-learning, agent-environment interaction, state-action values and policy improvement.

Prerequisites

Read SUT18 chapter 6 to gain knowledge about the mentioned topics and terms. SUT18 is the standard literature for reinforcment learning and the basis for this and following notebooks.

Python Modules

import gym
import numpy as np
import matplotlib.pyplot as plt

Frozenlake environment

env = gym.make('FrozenLake-v0')

env.reset()
env.render()

Tie-breaking argmax

def random_argmax_axis1(b):
    """ a random tie-breaking argmax"""
    return np.argmax(np.random.random(b.shape) * (b.T==b.max(axis=1)).T, axis=1)

##$ \epsilon $-greedy policy

def epsilon_policy(s,Q_sa,env,epsilon=0.2):
    
    if np.random.uniform(0,1) < epsilon:
        action = env.action_space.sample() #exploration
    else:
        action = random_argmax_axis1(Q_sa)[s] #explotation
    return action

Exercise

Task

Implement the Q-learning algorithm given in chapter 6.5 in SUT18.

def q_learning(env,nb_episode,alpha=0.5,gamma=0.95):
    
    """
    Args:
        env: given environment
        nb_episode: number of episodes used for training
    Kwargs:
        alpha: learning rate for Q-learning
        gamma: discount rate
        
    Return:
        Q_sa: learned Q-table
    """

    Q_sa = np.zeros((env.observation_space.n,env.action_space.n))

    #for e in range(nb_episode):
        
        #done = False
        #while not done:
            
            
            #generate steps
            
            #q_learning
            
            
    return NotImplementedError

Training the agent

Q_sa = q_learning(env,100000)

print(Q_sa)

Test performance after training

Since each performance test might lead to a different value accordingly to the random nature of our frozenlake environment due to its slippery condition, it is usefull to find the mean over many tests. Reaching over 0.7 means your learning was succesful.

greedy_policy = random_argmax_axis1(Q_sa)
print(greedy_policy)

policy = lambda s: greedy_policy[s]

def test_performance(policy, nb_episodes=100):
    sum_returns = 0
    for i in range(nb_episodes):
        state  = env.reset()
        done = False
        while not done:
            action = policy(state)
            state, reward, done, info = env.step(action)
            if done:
                sum_returns += reward
    return sum_returns/nb_episodes

mean_performance_list = []
mean_performance = 0
n = 300
for i in range(n):
    performance = test_performance(policy)
    mean_performance_list.append(performance)
    mean_performance += performance
    
print(mean_performance/n)

plt.hist(mean_performance_list,bins=30)
plt.grid()
plt.xlabel("Policy performance")
plt.show()

Literature

Licenses

Notebook License (CC-BY-SA 4.0)

The following license applies to the complete notebook, including code cells. It does however not apply to any referenced external media (e.g., images).

exercise-TD-q-learning-frozenlake-gym

Oliver Fischer

is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Based on a work at https://gitlab.com/deep.TEACHING.

Code License (MIT)

The following license only applies to code cells of the notebook.

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.