强化学习拟合一个函数的代码

下面是一个简单的强化学习拟合正弦函数的代码示例，使用的是 Python 和 PyTorch 框架：

import torch
import torch.nn as nn
import torch.optim as optim
import numpy as np

# 定义 Q-learning 网络
class QNet(nn.Module):
    def __init__(self):
        super(QNet, self).__init__()
        self.fc1 = nn.Linear(1, 10)
        self.fc2 = nn.Linear(10, 1)

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

# 定义环境
class Env:
    def __init__(self):
        self.x_min = 0
        self.x_max = 2 * np.pi

    def reset(self):
        self.x = np.random.uniform(self.x_min, self.x_max)
        return self.x

    def step(self, y):
        y_true = np.sin(self.x)
        reward = -((y - y_true) ** 2)
        self.x += 0.1 # 步长为 0.1
        done = self.x >= self.x_max
        return self.x, reward, done

# 训练模型
def train(model, env, optimizer, gamma=0.9, epochs=100):
    for epoch in range(epochs):
        state = env.reset()
        done = False
        while not done:
            state_tensor = torch.FloatTensor([state])
            q_values = model(state_tensor)
            action = q_values.argmax().item()
            y_pred = env.x
            next_state, reward, done = env.step(y_pred)
            next_state_tensor = torch.FloatTensor([next_state])
            next_q_values = model(next_state_tensor)
            max_q_value = next_q_values.max().item()
            target_q_value = reward + gamma * max_q_value
            loss = nn.MSELoss()(q_values[action], torch.FloatTensor([target_q_value]))
            optimizer.zero_grad()
            loss.backward()
            optimizer.step()
            state = next_state

# 测试模型
def test(model, env, n=100):
    mse = 0
    for i in range(n):
        state = env.reset()
        done = False
        while not done:
            state_tensor = torch.FloatTensor([state])
            q_values = model(state_tensor)
            action = q_values.argmax().item()
            y_pred = env.x
            next_state, reward, done = env.step(y_pred)
            mse += (y_pred - np.sin(state)) ** 2
            state = next_state
    print("MSE:", mse / n)

# 训练和测试
env = Env()
model = QNet()
optimizer = optim.Adam(model.parameters(), lr=0.01)
train(model, env, optimizer, epochs=10000)
test(model, env)

在这个例子中，我们定义了一个 Q-learning 网络和一个环境。Q-learning 网络用来估计状态-动作对的 Q 值函数，环境则用来生成状态和奖励。训练过程中，我们使用 Q-learning 算法来更新 Q 值函数，以尽可能地减小预测值与真实值之间的误差。测试过程中，我们使用一些测试数据来验证模型的预测准确性和泛化能力。