Q-learning

Reinforcement Learning with Gymnasium in Python

Fouad Trad

Machine Learning Engineer

Introduction to Q-learning

Stands for quality learning
Model-free technique
Learns optimal Q-table by interaction

Diagram showing the steps involved in Q-learning including initializing a Q-table, choosing an action to perform, receiving a reward from the environment, and updating the table. The agent continues this loop until convergence is achieved after a certain number of episodes.

Q-learning vs. SARSA

SARSA

Image showing the mathematical formula of the SARSA update rule.

Updates based on taken action
On-policy learner

Q-learning

Image showing the mathematical formula of the Q-learning update rule.

Updates independent of taken actions
Off-policy learner

Q-learning implementation

env = gym.make("FrozenLake", is_slippery=True)


num_episodes = 1000
alpha = 0.1
gamma = 1


num_states, num_actions = env.observation_space.n, env.action_space.n
Q = np.zeros((num_states, num_actions))


reward_per_random_episode = []

Q-learning implementation

for episode in range(num_episodes):
    state, info = env.reset()
    terminated = False
    episode_reward = 0

    while not terminated:

        # Random action selection
        action = env.action_space.sample()

        # Take action and observe new state and reward
        new_state, reward, terminated, truncated, info = env.step(action)

        # Update Q-table
        update_q_table(state, action, new_state)

        episode_reward += reward
        state = new_state

    reward_per_random_episode.append(episode_reward)

Q-learning update

Image showing the mathematical formula of the Q-learning update rule.

def update_q_table(state, action, reward, new_state):

  old_value = Q[state, action]

  next_max = max(Q[new_state])

  Q[state, action] = (1 - alpha) * old_value + alpha * (reward + gamma * next_max)

Using the policy

reward_per_learned_episode = []

policy = get_policy()

for episode in range(num_episodes):
    state, info = env.reset()
    terminated = False
    episode_reward = 0
    while not terminated:
        # Select the best action based on learned Q-table
        action = policy[state]
        # Take action and observe new state
        new_state, reward, terminated, truncated, info = env.step(action)
        state = new_state

        episode_reward += reward

    reward_per_learned_episode.append(episode_reward)

Q-learning evaluation

import numpy as np
import matplotlib.pyplot as plt


avg_random_reward = np.mean(reward_per_random_episode)
avg_learned_reward = np.mean(reward_per_learned_episode)


plt.bar(['Random Policy', 'Learned Policy'],
        [avg_random_reward, avg_learned_reward],
        color=['blue', 'green'])

plt.title('Average Reward per Episode')
plt.ylabel('Average Reward')
plt.show()

Image of a bar plot showing that the learned policy yields a much higher return (around 0.26)than the random policy (around 0.01).

Let's practice!

Reinforcement Learning with Gymnasium in Python