DQN-深度Q网络

深度Q网络是用深度学习来解决强化中Q学习的问题，可以先了解一下Q学习的过程是一个怎样的过程，实际上就是不断的试错，从试错的经验之中寻找最优解

关于Q学习，我看到一个非常好的例子，另外知乎上面也有相关的讨论

其实早在13年的时候，deepmind出来了第一篇用深度学习来解决Q学习的问题的paper，那个时候deepmind还不够火，和一般的Q学习不同的是，由于12年Alex率先用CNN解决图像中的high level的语义的提取，deepmind也同时采用了CNN来直接对图像进行特征提取，而非传统的进行手工特征提取

我想从代码的角度来看一下DQN是如何实现的

pytorcyh的代码在官网上是有的，我也贴出了自己添加了注释的代码，以及写一下自己的对于代码的理解

 # -*-coding:utf-8-*-
 import gym
 import math
 import random
 import numpy as np
 import matplotlib
 import matplotlib.pyplot as plt
 from collections import namedtuple
 from itertools import count
 from PIL import Image

 import torch
 import torch.nn as nn
 import torch.optim as optim
 import torch.nn.functional as F
 import torchvision.transforms as T

 env = gym.make('CartPole-v0').unwrapped

 # set up matplotlib
 is_ipython = 'inline' in matplotlib.get_backend()
 if is_ipython:
     from IPython import display

 plt.ion()

 # if gpu is to be used
 # device = torch.device("cuda" if torch.cuda.is_available() else "cpu")

 Transition = namedtuple('Transition',
                         ('state', 'action', 'next_state', 'reward'))  # 声明一个name为Transition，里面的变量为以下的类似dict的

 class ReplayMemory(object):

     def __init__(self, capacity):
         self.capacity = capacity
         self.memory = []
         self.position = 0

     def push(self, *args):
         """Saves a transition."""
         if len(self.memory) < self.capacity:
             self.memory.append(None)
         self.memory[self.position] = Transition(*args)
         self.position = (self.position + 1) % self.capacity

     def sample(self, batch_size):
         return random.sample(self.memory, batch_size)

     def __len__(self):  # 定义__len__以便于用len函数？
         return len(self.memory)

 class DQN(nn.Module):

     def __init__(self):
         super(DQN, self).__init__()
         self.conv1 = nn.Conv2d(3, 16, kernel_size=5, stride=2)
         self.bn1 = nn.BatchNorm2d(16)
         self.conv2 = nn.Conv2d(16, 32, kernel_size=5, stride=2)
         self.bn2 = nn.BatchNorm2d(32)
         self.conv3 = nn.Conv2d(32, 32, kernel_size=5, stride=2)
         self.bn3 = nn.BatchNorm2d(32)
         self.head = nn.Linear(448, 2)

     def forward(self, x):
         x = F.relu(self.bn1(self.conv1(x)))
         x = F.relu(self.bn2(self.conv2(x)))
         x = F.relu(self.bn3(self.conv3(x)))
         return self.head(x.view(x.size(0), -1))

 resize = T.Compose([T.ToPILImage(),
                     T.Resize(40, interpolation=Image.CUBIC),
                     T.ToTensor()])

 # This is based on the code from gym.
 screen_width = 600

 def get_cart_location():
     world_width = env.x_threshold * 2
     scale = screen_width / world_width
     return int(env.state[0] * scale + screen_width / 2.0)  # MIDDLE OF CART

 def get_screen():
     screen = env.render(mode='rgb_array').transpose(
         (2, 0, 1))  # transpose into torch order (CHW)
     # Strip off the top and bottom of the screen
     screen = screen[:, 160:320]
     view_width = 320
     cart_location = get_cart_location()
     if cart_location < view_width // 2:
         slice_range = slice(view_width)
     elif cart_location > (screen_width - view_width // 2):
         slice_range = slice(-view_width, None)
     else:
         slice_range = slice(cart_location - view_width // 2,
                             cart_location + view_width // 2)
     # Strip off the edges, so that we have a square image centered on a cart
     screen = screen[:, :, slice_range]
     # Convert to float, rescare, convert to torch tensor
     # (this doesn't require a copy)
     screen = np.ascontiguousarray(screen, dtype=np.float32) / 255
     screen = torch.from_numpy(screen)
     # Resize, and add a batch dimension (BCHW)
     return resize(screen).unsqueeze(0).cuda()

 env.reset()
 # plt.figure()
 # plt.imshow(get_screen().cpu().squeeze(0).permute(1, 2, 0).numpy(),
 #            interpolation='none')
 # plt.title('Example extracted screen')
 # plt.show()
 BATCH_SIZE = 128
 GAMMA = 0.999
 EPS_START = 0.9
 EPS_END = 0.05
 EPS_DECAY = 200
 TARGET_UPDATE = 10

 policy_net = DQN().cuda()
 target_net = DQN().cuda()
 target_net.load_state_dict(policy_net.state_dict())
 target_net.eval()

 optimizer = optim.RMSprop(policy_net.parameters())
 memory = ReplayMemory(10000)

 steps_done = 0

 def select_action(state):
     global steps_done
     sample = random.random()
     eps_threshold = EPS_END + (EPS_START - EPS_END) * \
         math.exp(-1. * steps_done / EPS_DECAY)
     steps_done += 1
     if sample > eps_threshold:
         with torch.no_grad():
             return policy_net(state).max(1)[1].view(1, 1)  # policy网络的输出
     else:
         return torch.tensor([[random.randrange(2)]], dtype=torch.long).cuda()  # 随机的选择一个网络的输出或者

 episode_durations = []

 def plot_durations():
     plt.figure(2)
     plt.clf()
     durations_t = torch.tensor(episode_durations, dtype=torch.float)
     plt.title('Training...')
     plt.xlabel('Episode')
     plt.ylabel('Duration')
     plt.plot(durations_t.numpy())
     # Take 100 episode averages and plot them too
     if len(durations_t) >= 100:
         means = durations_t.unfold(0, 100, 1).mean(1).view(-1)
         means = torch.cat((torch.zeros(99), means))
         plt.plot(means.numpy())

     plt.pause(0.001)  # pause a bit so that plots are updated
     if is_ipython:
         display.clear_output(wait=True)
         display.display(plt.gcf())

 def optimize_model():
     if len(memory) < BATCH_SIZE:
         return
     transitions = memory.sample(BATCH_SIZE)  # 进行随机的sample，序列问题是不存在的
     # print(transitions)
     # Transpose the batch (see http://stackoverflow.com/a/19343/3343043 for
     # detailed explanation).
     batch = Transition(*zip(*transitions))
     # print("current")
     # print(batch.state[0])
     # print("next")
     # print(batch.next_state[0])
     # print(torch.sum(batch.state[0]))
     # print(torch.sum(batch.next_state[0]))
     # print(torch.sum(batch.state[1]))
     # # print(type(batch))
     # print("@#$%^&*")

     # Compute a mask of non-final states and concatenate the batch elements
     non_final_mask = torch.tensor(tuple(map(lambda s: s is not None, batch.next_state)), dtype=torch.uint8).cuda()  # lambda表达式返回的是否为空的二值
     non_final_next_states = torch.cat([s for s in batch.next_state if s is not None])  # 空的不cat，所以长度不一定是batchsize
     # print("the non_final_mask is")
     # print(non_final_mask)
     # none_total = 0
     # total = 0
     # for s in batch.next_state:
     #     if s is None:
     #         none_total = none_total + 1
     #     else:
     #         total = total + 1
     # print(none_total, total)
     state_batch = torch.cat(batch.state)
     action_batch = torch.cat(batch.action)
     reward_batch = torch.cat(batch.reward)
     # print(action_batch)  # 非0即1
     # print(reward_batch)
     # print(len(non_final_mask))
     # Compute Q(s_t, a) - the model computes Q(s_t), then we select the
     # columns of actions taken
     state_action_values = policy_net(state_batch).gather(1, action_batch)  # gather将torch.tensor的中对应于action的index取出，dim为1
     # 从整体公式上而言，Q函数的值即为state_action_value的值
     # print((policy_net(state_batch)))
     # print(state_action_values)
     # Compute V(s_{t+1}) for all next states.
     next_state_values = torch.zeros(BATCH_SIZE).cuda()
     # print(next_state_values)
     # print("no final mask")
     # print(non_final_mask)
     # print("@#$%^&*")
     next_state_values[non_final_mask] = target_net(non_final_next_states).max(1)[0].detach()  # non_final_mask为1的地方进行赋值操作，其余仍为0
     # print(target_net(non_final_next_states).max(1)[0].detach())
     # print("12345")
     # print(next_state_values)
     # Compute the expected Q values
     expected_state_action_values = (next_state_values * GAMMA) + reward_batch

     # Compute Huber loss
     loss = F.smooth_l1_loss(state_action_values, expected_state_action_values.unsqueeze(1))

     # compare the parameters of 2 networks
     print(policy_net.state_dict()['head.bias'])
     print("!@#$%^&*")
     print(target_net.state_dict()['head.bias'])

     # Optimize the model
     optimizer.zero_grad()
     loss.backward()
     for param in policy_net.parameters():
         param.grad.data.clamp_(-1, 1)
     optimizer.step()

 num_episodes = 50
 for i_episode in range(num_episodes):
     # print("the episode is %f" % i_episode)
     # Initialize the environment and state
     env.reset()
     last_screen = get_screen()
     # print(last_screen)
     # print("#QW&*!$")
     current_screen = get_screen()  # 得到一张图片，而非一个batch
     # print(current_screen)
     state = current_screen - last_screen  # 两帧之间的差值，作为一个state，并且输入网络，类比于RNN对pose的估计
     for t in count():  # 创建一个无限循环迭代器，t的数值会一直增加
         # Select and perform an action
         action = select_action(state)
         _, reward, done, _ = env.step(action.item())  # done表示游戏是否结束, reward由gym内部决定；输入action，gym展示下一个状态
         reward = torch.tensor([reward]).cuda()

         # Observe new state
         last_screen = current_screen
         current_screen = get_screen()
         if not done:
             next_state = current_screen - last_screen
         else:
             next_state = None

         # Store the transition in memory
         memory.push(state, action, next_state, reward)  # memory存储state，action，next_state,以及对应的reward
         # print("the length of the memory is %d" % len(memory))
         # Move to the next state
         state = next_state

         # Perform one step of the optimization (on the target network)
         optimize_model()
         if done:
             episode_durations.append(t + 1)
             plot_durations()
             break
     # Update the target network
     if i_episode % TARGET_UPDATE == 0:  # 只有在某个频率下才会update target网络结构
         target_net.load_state_dict(policy_net.state_dict())

 print('Complete')
 env.render()
 env.close()
 plt.ioff()
 plt.show()
 env.close()

作者调用了一个gym的库，这个库可以用作强化学习的训练样本，但是蛋疼的是，在用pycharm进行debug的时候，gym库总会报错，如果直接运行则不会，我想可能是因为gym库并不可以进行调试

anyway，代码的总体流程是，调用gym，声明一个事件，在强化学习中被称为agent，这个agent会展示当前的状态，然后会接收一个action，输出下一个的状态以及这个action所得到的奖励，ok，至于这个agent采取了action之后所得到的奖励是如何计算的，

这个agent采取了这个action下一个状态是啥，gym已经给你们写好了

在定义网络结构之前，作者实际上是把自己试错的状态存储了起来，存储的内容有，当前的state，采取action，以及nextstate，以及这个action相应的reward，而state并不是当前游戏的截屏，而是两帧之间的差值，reward是gym自己返回的

至于为什么这样做？有点儿类似与用RNN解决slam的问题，为什么输入到网络中的是视频两帧之间的差值，而不是视频自己本身的内容，要给自己挖个坑

存储了这些状态之后就可以训练网络了，主体的网络结构如下

 class DQN(nn.Module):

     def __init__(self):
         super(DQN, self).__init__()
         self.conv1 = nn.Conv2d(3, 16, kernel_size=5, stride=2)
         self.bn1 = nn.BatchNorm2d(16)
         self.conv2 = nn.Conv2d(16, 32, kernel_size=5, stride=2)
         self.bn2 = nn.BatchNorm2d(32)
         self.conv3 = nn.Conv2d(32, 32, kernel_size=5, stride=2)
         self.bn3 = nn.BatchNorm2d(32)
         self.head = nn.Linear(448, 2)

     def forward(self, x):
         x = F.relu(self.bn1(self.conv1(x)))
         x = F.relu(self.bn2(self.conv2(x)))
         x = F.relu(self.bn3(self.conv3(x)))
         return self.head(x.view(x.size(0), -1))

网络输出的两个值，分别是对应不同的action，其实也不难理解，训练的网络最终能够产生的输出当然是决策是怎样的，不过这种自己不断的试错，并且把自己试错的数据保存下来，严格意义上来说真的是无监督学习？

anyway，作者用这些试错的数据进行训练

不过，网络的loss怎么设计？

loss如上，实际上就是求取两个Q函数之间的差值，ok，前一个Q函数的自变量描述的是当前的状态s以及对应的行为a，后一个r+Q描述的是当前的reward加上，在下一个state如何采取下一步行动能够让Q最大的项

而这两项如何在代码中体现，实际上作者定义了两个网络，一个成为policy，另外一个为target网络

优化的目标是policy net，target网络为定期对policy的copy，如下

     # Update the target network
     if i_episode % TARGET_UPDATE == 0:  # 只有在某个频率下才会update target网络结构
         target_net.load_state_dict(policy_net.state_dict())

policy net输入state batch，并且将实际中的对应的action的那一列输出，action非0即1,所以policy_net输出的是batch_size的列向量

在这段代码中，这个网络的输出就是Q函数的值，

target_net网络输入的是next_state，并且因为不知道其实际的action是多少，所以取最大的，输出乘以一个gamma，并且加上当前状态的reward即可

其实永远是policy_net更新在前，更新的方向是让两个网络的输出尽可能的接近，其实也不仅仅是这样，这中间还有一个reward变量，可是为什么target_net的更新要永远滞后，一种更加极端的情况是，如果把next_state输入到policy网络中呢？