Actor-Critic入门：原理、代码与案例演示 | Pytorch版

Actor-Critic算法是一种集成策略与价值迭代的强化学习方法。它通过分离行动者（Actor）与评论家（Critic）的角色，实现了高效策略学习与快速评估，为强化学习领域提供了强大的工具。本文将深入探讨Actor-Critic算法的原理，解析策略梯度与公式推导，通过Pytorch实现算法，并以OpenAI Gym的CartPole-v0环境为例，展示实际代码应用。

策略梯度算法

策略梯度算法直接优化策略函数，不依赖于价值函数。其核心在于通过策略梯度来修正策略参数，以提升策略性能。公式如下所示：

[ \nabla J(\theta) = \mathbb{E}{\tau\sim P(\tau|\theta)}\left[ \frac{Q(s,a|\theta)}{P(a|s,\theta)} \nabla{\theta}P(a|s,\theta) \right] ]

其中，(J(\theta))代表策略的性能度量，(Q(s,a|\theta))是动作(a)在状态(s)下的预期回报，而(P(a|s,\theta))是给定策略(\theta)下，动作(a)在状态(s)的出现概率。

Actor-Critic模型分解

Actor-Critic模型涵盖了两个关键部分：

• Actor：通常采用策略网络（如多层感知器或深度神经网络），根据当前环境状态(s)输出动作的概率分布(P(a|s))。
• Critic：评价网络（或价值网络），估计给定状态(s)或状态-动作对((s,a))的预期回报。通过状态价值(V(s))或动作价值(Q(s,a))提供反馈，指导策略更新。

Pytorch代码实现

下面，我们使用Pytorch构建一个简单的Actor-Critic模型：

import torch
import torch.nn as nn
import torch.nn.functional as F

class PolicyNet(nn.Module):
    def __init__(self, n_states, n_actions):
        super().__init__()
        self.fc1 = nn.Linear(n_states, 64)
        self.fc2 = nn.Linear(64, n_actions)

    def forward(self, x):
        x = F.relu(self.fc1(x))
        x = self.fc2(x)
        return F.softmax(x, dim=1)

class ValueNet(nn.Module):
    def __init__(self, n_states):
        super().__init__()
        self.fc1 = nn.Linear(n_states, 64)
        self.fc2 = nn.Linear(64, 1)

    def forward(self, x):
        x = F.relu(self.fc1(x))
        x = self.fc2(x)
        return x

class ActorCritic(nn.Module):
    def __init__(self, n_states, n_actions):
        super().__init__()
        self.actor = PolicyNet(n_states, n_actions)
        self.critic = ValueNet(n_states)

    def take_action(self, state):
        state = torch.tensor(state, dtype=torch.float32)
        probs = self.actor(state)
        m = torch.distributions.Categorical(probs)
        action = m.sample()
        return action.item()

    def update(self, transitions):
        states, actions, next_states, rewards, dones = map(torch.tensor, zip(*transitions))
        states = states.float()
        actions = actions.squeeze().long()
        rewards = rewards.float()
        dones = dones.float()

        values = self.critic(states)
        next_values = self.critic(next_states)
        td_targets = rewards + (next_values * 0.99 * (1 - dones))
        advantages = td_targets - values

        actor_loss = torch.mean(-actions * advantages.detach())
        critic_loss = torch.mean((values - td_targets.detach())**2)

        self.actor_optimizer.zero_grad()
        self.critic_optimizer.zero_grad()
        actor_loss.backward()
        critic_loss.backward()
        self.actor_optimizer.step()
        self.critic_optimizer.step()

应用Actor-Critic模型于OpenAI的CartPole-v0环境中，以下是简化的训练流程示例：

import gym
import torch

env = gym.make('CartPole-v1')
n_states = env.observation_space.shape[0]
n_actions = env.action_space.n

actor_lr = 0.001
critic_lr = 0.01
gamma = 0.99

actor = PolicyNet(n_states, n_actions)
critic = ValueNet(n_states)
actor_optimizer = torch.optim.Adam(actor.parameters(), lr=actor_lr)
critic_optimizer = torch.optim.Adam(critic.parameters(), lr=critic_lr)

def learn(env, actor, critic, actor_optimizer, critic_optimizer, gamma, num_episodes=1000):
    for episode in range(num_episodes):
        state = env.reset()
        done = False
        total_reward = 0
        while not done:
            action = actor.take_action(state)
            next_state, reward, done, _ = env.step(action)
            transition = (state, action, reward, next_state, done)
            total_reward += reward
            # 假设`update_networks`已包含完整更新逻辑
            # update_networks(transition, advantages)
            state = next_state
        print(f'Episode {episode}, Reward: {total_reward}')
    env.close()

通过集成策略迭代与价值迭代，Actor-Critic算法实现了在强化学习中的高效策略优化与快速评估。本文不仅详述了算法原理、公式推导，还提供了Pytorch实现的代码示例，通过实际的CartPole-v0环境案例，展示了算法在实践中的应用。未来，随着计算能力的增强与算法优化，Actor-Critic算法将在更多领域展现出其潜力，推动自动化、智能决策系统的发展，如机器人控制、自动驾驶与游戏智能体等领域。