最小構成のDQNアルゴリズム

Pythonで学ぶDeep Reinforcement Learning

Timothée Carayol

Principal Machine Learning Engineer, Komment

最小構成のDQN

 

 

  • 完全なDQNへの最初の一歩
  • 機能:
    • 汎用DRLトレーニングループ
    • Qネットワーク
    • Q学習の原理
for episode in range(1000):
  state, info = env.reset()
  done = False
  while not done:
    # Action selection
    action = select_action(network, state)
    next_state, reward, terminated, truncated, _ = (
                                   env.step(action))
    done = terminated or truncated
    # Loss calculation
    loss = calculate_loss(network, state, action, 
                          next_state, reward, done)
    optimizer.zero_grad()
    loss.backward()
    optimizer.step()
    state = next_state
Pythonで学ぶDeep Reinforcement Learning

最小構成DQNの行動選択

 

def select_action(q_network, state):

    # Feed state to network to obtain Q-values

    q_values = q_network(state)

    # Obtain index of action with highest Q-value
    action = torch.argmax(q_values).item()

    return action
  • 方策: 最大Q値の行動を選択
    • $ a_t = {\arg\max}_a Q(S_t, a) $
    • ここでは: 行動2、Q値は 0.12

 

 

Q-values: [-0.01, 0.08, 0.12, -0.07]

選択された行動: 2、q値 0.12
Pythonで学ぶDeep Reinforcement Learning

最小構成DQNの損失関数

 

  • 行動価値関数はベルマン方程式を満たす
  • 両辺の差（TD誤差/ベルマン誤差）を最小化
  • 二乗ベルマン誤差を損失として使用

DQN損失（二乗ベルマン誤差）: L(theta) = ベルマン誤差の二乗

 

ベルマン方程式 Q(S,A) = reward + discount * max(Q(S_next,A))

ベルマン誤差 Q(S,A) - (reward + discount * max(Q(S_next,A)))

Pythonで学ぶDeep Reinforcement Learning

最小構成DQNの損失関数

def calculate_loss(
      q_network, state, action,
      next_state, reward, done):

    q_values = q_network(state)

    current_state_q_value = q_values[action]

    next_state_q_value = q_network(next_state).max()

    target_q_value = reward +
                gamma * next_state_q_value * (1-done)

    loss = nn.MSELoss()(
              current_state_q_value, target_q_value)

    return loss
  • 現在状態のQ値:

       $Q(s_t, a_t)$

  • 次状態のQ値:

       $\max_a Q(s_{t+1}, a)$

  • 目標Q値:

       $r_{t+1} + \gamma \max_a Q(s_{t+1}, a)$

  • DQNの損失:

$$\left(Q(s_t, a_t) - (r_{t+1} + \gamma \max_a Q(s_{t+1}, a)\right)^2$$

Pythonで学ぶDeep Reinforcement Learning

エピソードの記述

describe_episode(episode, reward, episode_reward, step)

| Episode    1 | Duration:   84 steps | Return: -871.38 | Crashed  |

| Episode    2 | Duration:   53 steps | Return: -452.68 | Crashed  |

| Episode    3 | Duration:   57 steps | Return: -414.22 | Crashed  |
| Episode    4 | Duration:   54 steps | Return: -475.09 | Crashed  |

| Episode    5 | Duration:   67 steps | Return: -532.31 | Crashed  |
| Episode    6 | Duration:   53 steps | Return: -407.00 | Crashed  |
| Episode    7 | Duration:   52 steps | Return: -380.45 | Crashed  |
| Episode    8 | Duration:   55 steps | Return: -380.75 | Crashed  |
| Episode    9 | Duration:   88 steps | Return: -688.68 | Crashed  |
| Episode   10 | Duration:   76 steps | Return: -338.06 | Crashed  |
Pythonで学ぶDeep Reinforcement Learning

Ayo berlatih!

Pythonで学ぶDeep Reinforcement Learning

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