本章全篇参考赵世钰老师的教材 Mathmatical-Foundation-of-Reinforcement-Learning Deep Q-learning 章节，请各位结合阅读，本合集只专注于数学概念的代码实现。

DQN 算法

1）使用随机权重$（w\leftarrow 1.0）$初始化目标网络$Q(s,a,w)$和网络$\hat{Q}(s,a,w)$，$Q$和$\hat{Q}$相同，清空回放缓冲区。

2）以概率ε选择一个随机动作a，否则 $a=argmaxQ(s,a,w)$。

3）在模拟器中执行动作a，观察奖励r和下一个状态s’。

4）将转移过程(s, a, r, s’)存储在回放缓冲区中。

5）从回放缓冲区中采样一个随机的小批量转移过程。

6）对于回放缓冲区中的每个转移过程，如果片段在此步结束，则计算目标$y=r$，否则计算$y=r+\gamma max\hat{Q}(s,a,w)$ 。

7）计算损失：$L=(Q(s,a,w)–y{)}^2$。

8）固定网络$\hat{Q}(s,a,w)$不变，通过最小化模型参数的损失，使用SGD算法更新$Q(s,a)$。

9）每N步，将权重从目标网络$Q$复制到$\hat{Q}(s,a,w)$ 。

10）从步骤2开始重复，直到收敛为止。

定义DQN网络

import collections
import copy
import random
from collections import defaultdict
import math
import gym
import gym.spaces
import numpy as np
import torch
import torch.nn as nn
import torch.optim as optim
from gym.envs.toy_text import frozen_lake
from torch.utils.tensorboard import SummaryWriterclass Net(nn.Module):def __init__(self, obs_size, hidden_size, q_table_size):super(Net, self).__init__()self.net = nn.Sequential(# 输入为状态，样本为（1*n）nn.Linear(obs_size, hidden_size),nn.ReLU(),# nn.Linear(hidden_size, hidden_size),# nn.ReLU(),nn.Linear(hidden_size, q_table_size),)def forward(self, state):return self.net(state)class DQN:def __init__(self, env, tgt_net, net):self.env = envself.tgt_net = tgt_netself.net = netdef generate_train_data(self, batch_size, epsilon):state, _ = env.reset()train_data = []while len(train_data)<batch_size*2:q_table_tgt = self.tgt_net(torch.Tensor(state)).detach()if np.random.uniform(0, 1, 1) > epsilon:action = self.env.action_space.sample()else:action = int(torch.argmax(q_table_tgt))new_state, reward,terminated, truncted, info = env.step(action)train_data.append([state, action, reward, new_state, terminated])state = new_stateif terminated:state, _ = env.reset()continuerandom.shuffle(train_data)                return train_data[:batch_size]def calculate_y_hat_and_y(self, batch):# 6）对于回放缓冲区中的每个转移过程，如果片段在此步结束，则计算目标$y=r$，否则计算$y=r+\gamma max \hat Q(s, a, w)$ 。y = []state_space = []action_space = []for state, action, reward, new_state, terminated in batch:# y值if terminated:y.append(reward)else:# 下一步的 qtable 的最大值q_table_net = self.net(torch.Tensor(np.array([new_state]))).detach()y.append(reward + gamma * float(torch.max(q_table_net)))# y hat的值state_space.append(state)action_space.append(action)idx = [list(range(len(action_space))), action_space]y_hat = self.tgt_net(torch.Tensor(np.array(state_space)))[idx]return y_hat, torch.tensor(y)def update_net_parameters(self, update=True):self.net.load_state_dict(self.tgt_net.state_dict())

初始化环境

   # 初始化环境
env = gym.make("CartPole-v1")
# env = DiscreteOneHotWrapper(env)hidden_num = 64
# 定义网络
net = Net(env.observation_space.shape[0],hidden_num, env.action_space.n)
tgt_net = Net(env.observation_space.shape[0],hidden_num, env.action_space.n)
dqn = DQN(env=env, net=net, tgt_net=tgt_net)# 初始化参数
# dqn.init_net_and_target_net_weight()# 定义优化器
opt = optim.Adam(tgt_net.parameters(), lr=0.001)# 定义损失函数
loss = nn.MSELoss()# 记录训练过程
# writer = SummaryWriter(log_dir="logs/DQN", comment="DQN")

开始训练

gamma = 0.8
for i in range(10000):batch = dqn.generate_train_data(256, 0.8)y_hat, y = dqn.calculate_y_hat_and_y(batch)opt.zero_grad()l = loss(y_hat, y)l.backward()opt.step()print("MSE: {}".format(l.item()))if i % 5 == 0:dqn.update_net_parameters(update=True)

输出：

MSE: 0.027348674833774567
MSE: 0.1803671419620514
MSE: 0.06523636728525162
MSE: 0.08363766968250275
MSE: 0.062360599637031555
MSE: 0.004909628536552191
MSE: 0.05730309337377548
MSE: 0.03543371334671974
MSE: 0.08458714932203293

可视化结果

env = gym.make("CartPole-v1", render_mode = "human")
env = gym.wrappers.RecordVideo(env, video_folder="video")state, info = env.reset()
total_rewards = 0while True:q_table_state = dqn.tgt_net(torch.Tensor(state)).detach()# if np.random.uniform(0, 1, 1) > 0.9:#     action = env.action_space.sample()# else:action = int(torch.argmax(q_table_state))state, reward, terminated, truncted, info = env.step(action)if terminated:break