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一、带基线的REINFORCE

REINFORCE的优势在于只需要很小的更新步长就能收敛到局部最优，并保证了每次更新都是有利的，但是假设每个动作的奖赏均为正，则每个动作出现的概率将不断提高，这一现象会严重降低学习速率，并增大梯度方差

根据这一思想，我们构建一个仅与状态有关的基线函数，保证能够在不改变策略梯度的同时，降低其方差，带基线的REINFORCE算法是REINFORCE算法的改进版，原则上，与动作无关的函数都可以作为基线，但是为了对所有动作值都比较大的状态，需要设置一个较大的基线来区分最优动作和次优动作：对所有动作值都比较小的状态，则需要设置一个比较小的基线。由此用近似状态值函数代表基线，当回报超过基线值时，该动作的概率将提高，反之降低

二、结果与分析

1：实验环境设置

带基线的REINFORCE算法其网络结构，参数设置以及实验环境与REINFORCE一样，在算法中，近似状态值函数参数W的学习率为0.001，REINFORCE和带基线的REINFORCE效果对比如下图

在短走廊环境下，带基线的REINFORCE收敛的更快，并且更为稳定，

在CartPole环境下，两个算法的波动都比较大，带基线的更为明显，这是因为CartPole环境更为复杂。

三、代码

部分代码如下

import torch.nn as nnimport torch.nn.functional as Fimport gymimport torchfrom torch.distributions import Categoricalimport torch.optim as optimfrom copy import deepcopyimport numpy as npimport argparseimport matplotlib.pyplot as pltfrom _DUPLICATE_LIB_OK"]="True"render = Falseclass Policy(nn.Module):def __init__(self,n_states, n_hidden, n_output):super(Policy, self).__init__()self.linear1 = nn.Linear(n_states, n_hidden)self.linear2 = nn.Linear(n_hidden, n_output)#这是policy的参数self.reward = []self.log_act_probs = []self.Gt = []self.sigma = []#这是state_action_func的参数# self.Reward = []# self.s_value = []def forward(self, x):x = F.relu(self.linear1(x))output = F.softmax(self.linear2(x), dim= 1)# self.act_probs.append(action_probs)return outputenv = gym.make('CartPole-v0')n_states = env.observation_space.shape[0]n_actions = env.action_space.npolicy = Policy(n_states, 128, n_actions)s_value_func = Policy(n_states, 128, 1)alpha_theta = 1e-3optimizer_theta = optim.Adam(policy.parameters(), lr=alpha_theta)gamma = 0.99seed = 1e)plt.ylabel('Run Time')plt.plot(epi, run_time)plt.show()if __name__ == '__main__':running_reward = 10i_episodes = []for i_episode in range(1, 10000):state, ep_reward = env.reset(), 0if render: env.render()policy_loss = []s_value = []state_sequence = []log_act_prob = []for t in range(10000):state = torch.from_numpy(state).unsqueeze(0).float() # 在第0维增加一个维度，将数据组织成[N , .....] 形式state_sequence.append(deepcopy(state))action_probs = policy(state)m = Categorical(action_probs)action = m.sample()m_log_prob = m.log_prob(action)log_act_prob.append(m_log_prob)# policy.log_act_probs.append(m_log_prob)action = action.item()next_state, re, done, _ = env.step(action)if render: env.render()policy.reward.append(re)ep_reward += reif done:breakstate = next_staterunning_reward = 0.05 * ep_reward + (1 - 0.05) * running_rewardi_episodes.append(i_episode)if i_episode % 10 == 0:print('Episode {}\tLast length: {:2f}\tAverage length: {:.2f}'.format(i_episode, ep_reward, running_reward))live_time.append(running_reward)R = 0Gt = []# get Gt valuefor r in policy.reward[::-1]:R = r + gamma * RGt.insert(0, R)# update step by stepfor i in range(len(Gt)):G = Gt[i]V = s_value_func(state_sequence[i])delta = G - V# update value networkalpha_w = 1e-3 # 初始化optimizer_w = optim.Adam(s_value_func.parameters(), lr=alpha_w)optimizer_w.zero_grad()policy_loss_w = -deltapolicy_loss_w.backward(retain_graph=True)clip_grad_norm_(policy_loss_w, 0.1)optimizer_w.step()# update policy networkoptimizer_theta.zero_grad()policy_loss_theta = - log_act_prob[i] * deltapolicy_loss_theta.backward(retain_graph=True)clip_grad_norm_(policy_loss_theta, 0.1)optimizer_theta.step()del policy.log_act_probs[:]del policy.reward[:]if (i_episode % 1000 == 0):plot(i_episodes, live_time)np.save(f"withB", live_time)policy.plot(live_time)

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【PyTorch深度强化学习】带基线的蒙特卡洛策略梯度法（REINFOECE）在短走廊和CartPole环境下的实战（超详细 附源码）