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理论基础：

注意：

1. 策略的输出要加对数，因此net输出必须softmax，将输出限制为正数。

2. 这里选择action不是greedy地选择最优action，而是按照概率分布选择action->exploration。

3. 策略更新使用的是梯度上升，因此loss取负。

4. 这里使用step一步步收集episode，而不是像之前一样直接使用generate_episode函数生成完成的path，是因为在generate_episode中是使用greedy的方法选择action的（见2）。

5. num_episodes大一些。

代码可运行：

import numpy as np import torch from torch import nn from env import GridWorldEnv from utils import drow_policy ''' policy gradient by Monte Carlo ''' class Reinforce(object): def __init__(self, env: GridWorldEnv, gamma=0.9, lr=1e-2): ''' :param env: :param gamma: discount rate :param lr: learning rate of optimizer ''' self.env = env self.action_space_size = self.env.num_actions self.state_space_size = self.env.num_states self.gamma = gamma self.net = nn.Sequential( nn.Linear(2, 16), nn.ReLU(), nn.Linear(16, self.action_space_size) ) self.policy = np.zeros((self.state_space_size, self.action_space_size)) self.q_value = np.zeros((self.state_space_size, self.action_space_size)) self.optimizer = torch.optim.Adam(self.net.parameters(), lr=lr) def decode_state(self, state): ''' :param state: int :return: 归一化后的元组 ''' i = state // self.env.size j = state % self.env.size return torch.tensor((i / (self.env.size - 1), j / (self.env.size - 1)), dtype=torch.float32) def solve(self, num_episodes): for _ in range(num_episodes): state_int = self.env.reset() state = self.decode_state(state_int) done = False episode = [] # [[state_tensor,reward,done]...[...]] while not done: logits = self.net(state) action_probs = torch.softmax(logits, dim=0) action_dist = torch.distributions.Categorical(action_probs) # 按分布采样 action = action_dist.sample().item() next_state, reward, done = self.env.step(state_int, action) episode.append((state, action, reward)) state_int = next_state state = self.decode_state(next_state) # value update returns = [] G = 0 for _, _, reward in reversed(episode): G = reward + self.gamma * G returns.insert(0, G) # policy update self.optimizer.zero_grad() loss = 0 for (state, action, _), G in zip(episode, returns): logits = self.net(state) action_probs = torch.softmax(logits, dim=0) action_dist = torch.distributions.Categorical(action_probs) log_prob = action_dist.log_prob(torch.tensor(action)) # In Π(a_t|s_t, θ) loss -= log_prob * G # 负号是因为最小化 loss->最大化 J(θ)，梯度上升更新参数 loss.backward() self.optimizer.step() def get_policy(self): for s in range(self.state_space_size): a = np.argmax(self.q_value[s]) self.policy[s, a] = 1 return self.policy def get_qvalues(self): for s in range(self.state_space_size): s_t = self.decode_state(s) logits = self.net(s_t) action_probs = torch.softmax(logits, dim=0) self.q_value[s,:] = action_probs.detach().numpy() # q_value是numpy类型，action_probs是tensor，必须转换 return self.q_value if __name__ == '__main__': env = GridWorldEnv( size=5, forbidden=[(1, 2), (3, 3)], terminal=[(4, 4)], r_boundary=-1, r_other=-0.04, r_terminal=1, r_forbidden=-1, r_stay=-0.1 ) vi = Reinforce(env=env) vi.solve(num_episodes=200) print("\n state value: ") print(vi.get_qvalues()) drow_policy(vi.get_policy(), env)

运行结果：