Q学習

Pythonで学ぶGymnasiumによるReinforcement Learning

Fouad Trad

Machine Learning Engineer

Q学習の概要

「quality learning」の略
モデルフリー手法
相互作用で最適Qテーブルを学習

Qテーブルの初期化、行動の選択、環境からの報酬の受け取り、テーブル更新というQ学習の流れ。一定のエピソード後に収束。

Q学習 vs. SARSA

SARSA

SARSAの更新則の数式を示す画像。

実際に取った行動で更新
オンポリシー学習

Q学習

Q学習の更新則の数式を示す画像。

取った行動に依存せず更新
オフポリシー学習

Q学習の実装

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学習の実装

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学習の更新

Q学習の更新則の数式を示す画像。

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)

ポリシーの適用

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学習の評価

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()

学習済みポリシーの収益（約0.26）がランダムポリシー（約0.01）を大きく上回ることを示す棒グラフ。

演習に進みましょう！

Pythonで学ぶGymnasiumによるReinforcement Learning