❀DQN算法原理

DQN，Deep Q Network本质上还是Q learning算法，它的算法精髓还是让 $Q_{估计}$ 尽可能接近 $Q_{现实}$ ，或者说是让当前状态下预测的Q值跟基于过去经验的Q值尽可能接近。在后面的介绍中 $Q_{现实}$ 也被称为TD Target

再来回顾下DQN算法和核心思想
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相比于Q Table形式，DQN算法用神经网络学习Q值。
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我们可以理解为神经网络是一种估计方法，神经网络本身不是DQN的精髓，神经网络可以设计成MLP也可以设计成CNN等等，DQN的巧妙之处在于两个网络、经验回放等trick

下面介绍下DQN算法的一些trick，是希望帮助小伙伴们梳理区分两个网络的作用，阐述清楚经验回放等概念的本质，以及使用它们训练网络的技巧

Trick 1：两个网络

DQN算法采用了2个神经网络，分别是evaluate network（Q值网络）和target network（目标网络），两个网络结构完全相同

evaluate network用用来计算策略选择的Q值和Q值迭代更新，梯度下降、反向传播的也是evaluate network
target network用来计算TD Target中下一状态的Q值，网络参数更新来自evaluate network网络参数复制

设计target network目的是为了保持目标值稳定，防止过拟合，从而提高训练过程稳定和收敛速度

这里会有容易混淆的地方，梯度更新的是evaluate network的参数，不更新target network，然后每隔一段时间将evaluate network的网络参数复制给target network网络参数，那么优化器optimizer设置的时候用的也是evaluate network的parameters

Trick 2：基本框架

算法分成两个部分，分别是策略选择和策略评估，这也是强化学习算法基本的两个模块，梳理算法逻辑的时候从策略选择和策略评估两个方面入手，更容易弄清楚。策略选择部分，epsilon-greedy策略选择动作，策略评估部分使用贪婪策略

Trick 3：经验回放Experience Replay

DQN算法设计了一个固定大小的记忆库memory，用来记录经验，经验是一条一条的observation或者说是transition，它表示成 $[s, a, r, s^{'}]$ ，含义是当前状态→当前状态采取的动作→获得的奖励→转移到下一个状态

一开始记忆库memory中没有经验，也没有训练evaluate network，积累了一定数量的经验之后，再开始训练evaluate network。记忆库memory中的经验可以是自己历史的经验（epsilon-greedy得到的经验），也可以学习其他人的经验。训练evaluate network的时候，是从记忆库memory中随机选择（划重点哦，是随机选择!）batch size大小的经验，喂给evaluate network

设计记忆库memory并且随机选择经验喂给evaluate network的技巧打破了相邻训练样本之间相关性，试着想下，状态→动作→奖励→下一个状态的循环是具有关联的，用相邻的样本连续训练evaluate network会带来网络过拟合泛化能力差的问题，而经验回放技巧增强了训练样本之间的独立性

❀算法流程图

每个episode流程是下面这样
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其中choose_action、store_transition、learn是相互独立的函数模块，它们内部的算法逻辑是下面这样
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❀Pytorch版本代码

采用Pytorch实现了DQN算法，完成了走迷宫Maze游戏，哈哈哈，这个游戏来自莫烦Python教程，代码嘛是自己修改过哒，代码贴在github上啦

ningmengzhihe/DQN_base: DQN algorithm by Pytorch - a simple maze game https://github.com/ningmengzhihe/DQN_base

（1）环境构建代码maze_env.py


import numpy as np
import time
import sys
if sys.version_info.major == 2:
    import Tkinter as tk
else:
    import tkinter as tk

UNIT = 40   # pixels
MAZE_H = 4  # grid height
MAZE_W = 4  # grid width


class Maze(tk.Tk, object):
    def __init__(self):
        super(Maze, self).__init__()
        self.action_space = ['u', 'd', 'l', 'r']
        self.n_actions = len(self.action_space)
        self.n_features = 2
        self.title('maze')
        self.geometry('{0}x{1}'.format(MAZE_W * UNIT, MAZE_H * UNIT))
        self._build_maze()

    def _build_maze(self):
        self.canvas = tk.Canvas(self, bg='white',
                           height=MAZE_H * UNIT,
                           width=MAZE_W * UNIT)

        # create grids
        for c in range(0, MAZE_W * UNIT, UNIT):
            x0, y0, x1, y1 = c, 0, c, MAZE_H * UNIT
            self.canvas.create_line(x0, y0, x1, y1)
        for r in range(0, MAZE_H * UNIT, UNIT):
            x0, y0, x1, y1 = 0, r, MAZE_W * UNIT, r
            self.canvas.create_line(x0, y0, x1, y1)

        # create origin
        origin = np.array([20, 20])

        # hell
        hell1_center = origin + np.array([UNIT * 2, UNIT])
        self.hell1 = self.canvas.create_rectangle(
            hell1_center[0] - 15, hell1_center[1] - 15,
            hell1_center[0] + 15, hell1_center[1] + 15,
            fill='black')
        # hell
        # hell2_center = origin + np.array([UNIT, UNIT * 2])
        # self.hell2 = self.canvas.create_rectangle(
        #     hell2_center[0] - 15, hell2_center[1] - 15,
        #     hell2_center[0] + 15, hell2_center[1] + 15,
        #     fill='black')

        # create oval
        oval_center = origin + UNIT * 2
        self.oval = self.canvas.create_oval(
            oval_center[0] - 15, oval_center[1] - 15,
            oval_center[0] + 15, oval_center[1] + 15,
            fill='yellow')

        # create red rect
        self.rect = self.canvas.create_rectangle(
            origin[0] - 15, origin[1] - 15,
            origin[0] + 15, origin[1] + 15,
            fill='red')

        # pack all
        self.canvas.pack()

    def reset(self):
        self.update()
        time.sleep(0.1)
        self.canvas.delete(self.rect)
        origin = np.array([20, 20])
        self.rect = self.canvas.create_rectangle(
            origin[0] - 15, origin[1] - 15,
            origin[0] + 15, origin[1] + 15,
            fill='red')
        # return observation
        return (np.array(self.canvas.coords(self.rect)[:2]) - np.array(self.canvas.coords(self.oval)[:2]))/(MAZE_H*UNIT)

    def step(self, action):
        s = self.canvas.coords(self.rect)
        base_action = np.array([0, 0])
        if action == 0:   # up
            if s[1] > UNIT:
                base_action[1] -= UNIT
        elif action == 1:   # down
            if s[1] < (MAZE_H - 1) * UNIT:
                base_action[1] += UNIT
        elif action == 2:   # right
            if s[0] < (MAZE_W - 1) * UNIT:
                base_action[0] += UNIT
        elif action == 3:   # left
            if s[0] > UNIT:
                base_action[0] -= UNIT

        self.canvas.move(self.rect, base_action[0], base_action[1])  # move agent

        next_coords = self.canvas.coords(self.rect)  # next state

        # reward function
        if next_coords == self.canvas.coords(self.oval):
            reward = 1
            done = True
        elif next_coords in [self.canvas.coords(self.hell1)]:
            reward = -1
            done = True
        else:
            reward = 0
            done = False
        s_ = (np.array(next_coords[:2]) - np.array(self.canvas.coords(self.oval)[:2]))/(MAZE_H*UNIT)
        return s_, reward, done

    def render(self):
        # time.sleep(0.01)
        self.update()

（2）DQN算法代码，包括神经网络定义、Q值更新：RL_brain.py

"""
Deep Q Network off-policy
"""
import torch
import torch.nn as nn
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

np.random.seed(42)
torch.manual_seed(2)


class Network(nn.Module):
    """
    Network Structure
    """
    def __init__(self,
                 n_features,
                 n_actions,
                 n_neuron=10
                 ):
        super(Network, self).__init__()
        self.net = nn.Sequential(
            nn.Linear(in_features=n_features, out_features=n_neuron, bias=True),
            nn.Linear(in_features=n_neuron, out_features=n_actions, bias=True),
            nn.ReLU()
        )

    def forward(self, s):
        """

        :param s: s
        :return: q
        """
        q = self.net(s)
        return q


class DeepQNetwork(nn.Module):
    """
    Q Learning Algorithm
    """
    def __init__(self,
                 n_actions,
                 n_features,
                 learning_rate=0.01,
                 reward_decay=0.9,
                 e_greedy=0.9,
                 replace_target_iter=300,
                 memory_size=500,
                 batch_size=32,
                 e_greedy_increment=None):
        super(DeepQNetwork, self).__init__()

        self.n_actions = n_actions
        self.n_features = n_features
        self.lr = learning_rate
        self.gamma = reward_decay
        self.epsilon_max = e_greedy
        self.replace_target_iter = replace_target_iter
        self.memory_size = memory_size
        self.batch_size = batch_size
        self.epsilon_increment = e_greedy_increment
        self.epsilon = 0 if e_greedy_increment is not None else self.epsilon_max

        # total learning step
        self.learn_step_counter = 0

        # initialize zero memory [s, a, r, s_]
        # 这里用pd.DataFrame创建的表格作为memory
        # 表格的行数是memory的大小，也就是transition的个数
        # 表格的列数是transition的长度，一个transition包含[s, a, r, s_]，其中a和r分别是一个数字，s和s_的长度分别是n_features
        self.memory = pd.DataFrame(np.zeros((self.memory_size, self.n_features*2+2)))

        # build two network: eval_net and target_net
        self.eval_net = Network(n_features=self.n_features, n_actions=self.n_actions)
        self.target_net = Network(n_features=self.n_features, n_actions=self.n_actions)
        self.loss_function = nn.MSELoss()
        self.optimizer = torch.optim.Adam(self.eval_net.parameters(), lr=self.lr)

        # 记录每一步的误差
        self.cost_his = []


    def store_transition(self, s, a, r, s_):
        if not hasattr(self, 'memory_counter'):
            # hasattr用于判断对象是否包含对应的属性。
            self.memory_counter = 0

        transition = np.hstack((s, [a,r], s_))

        # replace the old memory with new memory
        index = self.memory_counter % self.memory_size
        self.memory.iloc[index, :] = transition

        self.memory_counter += 1

    def choose_action(self, observation):
        observation = observation[np.newaxis, :]

        if np.random.uniform() < self.epsilon:
            # forward feed the observation and get q value for every actions
            s = torch.FloatTensor(observation)
            actions_value = self.eval_net(s)
            action = [np.argmax(actions_value.detach().numpy())][0]
        else:
            action = np.random.randint(0, self.n_actions)
        return action

    def _replace_target_params(self):
        # 复制网络参数
        self.target_net.load_state_dict(self.eval_net.state_dict())

    def learn(self):
        # check to replace target parameters
        if self.learn_step_counter % self.replace_target_iter == 0:
            self._replace_target_params()
            print('\ntarget params replaced\n')

        # sample batch memory from all memory
        batch_memory = self.memory.sample(self.batch_size) \
            if self.memory_counter > self.memory_size \
            else self.memory.iloc[:self.memory_counter].sample(self.batch_size, replace=True)

        # run the nextwork
        s = torch.FloatTensor(batch_memory.iloc[:, :self.n_features].values)
        s_ = torch.FloatTensor(batch_memory.iloc[:, -self.n_features:].values)
        q_eval = self.eval_net(s)
        q_next = self.target_net(s_)

        # change q_target w.r.t q_eval's action
        q_target = q_eval.clone()

        # 更新值
        batch_index = np.arange(self.batch_size, dtype=np.int32)
        eval_act_index = batch_memory.iloc[:, self.n_features].values.astype(int)
        reward = batch_memory.iloc[:, self.n_features + 1].values

        q_target[batch_index, eval_act_index] = torch.FloatTensor(reward) + self.gamma * q_next.max(dim=1).values

        # train eval network
        loss = self.loss_function(q_target, q_eval)
        self.optimizer.zero_grad()
        loss.backward()
        self.optimizer.step()

        self.cost_his.append(loss.detach().numpy())

        # increasing epsilon
        self.epsilon = self.epsilon + self.epsilon_increment if self.epsilon < self.epsilon_max else self.epsilon_max
        self.learn_step_counter += 1

    def plot_cost(self):
        plt.figure()
        plt.plot(np.arange(len(self.cost_his)), self.cost_his)
        plt.show()

（3）每个episode代码：run_this.py

from maze_env import Maze
from RL_brain import DeepQNetwork

def run_maze():
    step = 0  # 为了记录走到第几步，记忆录中积累经验（也就是积累一些transition）之后再开始学习
    for episode in range(200):
        # initial observation
        observation = env.reset()

        while True:
            # refresh env
            env.render()

            # RL choose action based on observation
            action = RL.choose_action(observation)

            # RL take action and get next observation and reward
            observation_, reward, done = env.step(action)

            # !! restore transition
            RL.store_transition(observation, action, reward, observation_)

            # 超过200条transition之后每隔5步学习一次
            if (step > 200) and (step % 5 == 0):
                RL.learn()

            # swap observation
            observation = observation_

            # break while loop when end of this episode
            if done:
                break
            step += 1

    # end of game
    print("game over")
    env.destroy()


if __name__ == "__main__":
    # maze game
    env = Maze()
    RL = DeepQNetwork(env.n_actions, env.n_features,
                      learning_rate=0.01,
                      reward_decay=0.9,
                      e_greedy=0.9,
                      replace_target_iter=200,
                      memory_size=2000)
    env.after(100, run_maze)
    env.mainloop()
    RL.plot_cost()