CQL算法CartPole-v1

### CQL算法简介

保守Q学习(Conservative Q-Learning, CQL)是一种旨在解决离线强化学习中过估计问题的方法[^2]。通过引入额外的损失项来惩罚模型对于未见过的状态动作对过于乐观的价值评估，从而使得策略更加稳健。

### 应用于CartPole-v1环境中的CQL算法实现

为了在`CartPole-v1`环境中应用CQL算法，可以采用如下Python代码框架：

import gymnasium as gym
import numpy as np
import torch
from torch import nn, optim


class SimpleNN(nn.Module):
    def __init__(self, input_dim=4, hidden_dim=64, output_dim=2):
        super(SimpleNN, self).__init__()
        self.fc = nn.Sequential(
            nn.Linear(input_dim, hidden_dim),
            nn.ReLU(),
            nn.Linear(hidden_dim, hidden_dim),
            nn.ReLU(),
            nn.Linear(hidden_dim, output_dim)
        )

    def forward(self, x):
        return self.fc(x)


def cql_loss(q_values, actions_taken, rewards_received, next_states, dones, gamma=0.99, alpha=1.0):
    current_q_value = q_values.gather(-1, actions_taken.unsqueeze(-1)).squeeze()
    
    with torch.no_grad():
        next_state_max_q = q_network(next_states).max(dim=-1)[0]
        target_q_value = rewards_received + (1 - dones.float()) * gamma * next_state_max_q
    
    td_error = ((current_q_value - target_q_value)**2).mean()

    random_actions = torch.randint_like(actions_taken, low=0, high=q_values.shape[-1])
    data_actions = actions_taken.clone().detach()
    policy_actions = q_values.argmax(dim=-1)

    logsumexp_random = torch.logsumexp(q_values / alpha, dim=-1).mean() * alpha
    logsumexp_data = q_values.gather(-1, data_actions.unsqueeze(-1)).squeeze().mean()
    logsumexp_policy = q_values.gather(-1, policy_actions.unsqueeze(-1)).squeeze().mean()

    conservative_term = (
        logsumexp_random -
        0.5 * (logsumexp_data + logsumexp_policy)
    ).clamp(min=0.).mean()

    total_loss = td_error + conservative_term
    return total_loss


env = gym.make('CartPole-v1')
q_network = SimpleNN()
optimizer = optim.Adam(q_network.parameters(), lr=3e-4)

for episode in range(1000):  # 训练循环次数可根据需求调整
    state, _ = env.reset()
    done = False
    while not done:
        action = ...  # 这里应该根据当前状态选择行动；此处省略具体逻辑
        
        next_state, reward, terminated, truncated, info = env.step(action)
        done = terminated or truncated
        
        optimizer.zero_grad()
        
        states_tensor = ...
        actions_tensor = ...
        rewards_tensor = ...
        next_states_tensor = ...
        dones_tensor = ...

        loss = cql_loss(..., ..., ..., ..., ...)
        loss.backward()
        optimizer.step()

        state = next_state

上述代码片段展示了如何构建一个简单的神经网络作为价值函数近似器，并定义了一个基于TD误差以及保守性的损失函数来进行参数更新。需要注意的是，在实际操作过程中还需要考虑数据集准备、批量处理等多个方面的问题[^3]。