深度强化学习(DRL 3) - 从Q-learning到Deep Q Network(DQN)

目录一、Q-learning 二、Deep Q Network 三、Double DQN 一、Q-learning 关于Q-learning，网上的资料很多。 Q-learning最核心的是有一个Q表，它记录了在环境中的所有状态(s) 以及每个状态可以进行的所有行为(a) 的Q值，初值设为0。状态 \ 行为 a1 a2 a3 a4 s1 s2 s3 …… Q值的更新公式如下： Q ( s ...

一、Q-learning

关于Q-learning，网上的资料很多。

在这里插入图片描述

Q-learning最核心的是有一个Q表，它记录了在环境中的 所有状态(s) 以及每个状态可以进行的 所有行为(a) 的Q值，初值设为0。

状态 \ 行为	a1	a2	a3	a4
s1
s2
s3
……

Q值的更新公式如下：

$Q(s,a)←Q(s,a)+α[r+\gamma max_{a'}Q(s^′,a^′)−Q(s,a)]$

其中 $α$ 表示学习速率，取值小于1
$r$ 是设置的奖励
智能体在状态s经过行为a转移到状态s’， $max_{a'}Q(s^′,a^′)$ 是状态 $s^{'}$ 那一行最大Q值
$\gamma$ 则是衰减速率，取值在0到1之间， $\gamma$ 越大，智能体就会越注重长期利益， $\gamma$ 越小，智能体越短视。

每改变一次状态就会更新一次Q值

Q-learning 是一个 off-policy 的算法，它可以离线学习。它可以随机进行若干次游戏，将游戏过程保存起来，学习的时候就可以避免陷入局部最优。

Q-learning 的代码实现：

# -*- coding: UTF-8 -*-
import numpy as np
import pandas as pd


class QLearningTable:
    def __init__(self, actions, learning_rate=0.01, reward_decay=0.9, e_greedy=0.9):
        self.actions = actions  # a list
        self.lr = learning_rate
        self.gamma = reward_decay
        self.epsilon = e_greedy
        self.q_table = pd.DataFrame(columns=self.actions, dtype=np.float64)

    def choose_action(self, observation):
        self.check_state_exist(observation)
        # action selection
        if np.random.uniform() < self.epsilon:
            # choose best action
            state_action = self.q_table.loc[observation, :]
            state_action = state_action.reindex(np.random.permutation(state_action.index))     # some actions have same value
            action = state_action.idxmax()
        else:
            # choose random action
            action = np.random.choice(self.actions)
        return action

    def learn(self, s, a, r, s_):
        self.check_state_exist(s_)
        q_predict = self.q_table.loc[s, a]
        if s_ != 'terminal':
            q_target = r + self.gamma * self.q_table.loc[s_, :].max()  # next state is not terminal
        else:
            q_target = r  # next state is terminal
        self.q_table.loc[s, a] += self.lr * (q_target - q_predict)  # update

    def check_state_exist(self, state):
        if state not in self.q_table.index:
            # append new state to q table
            self.q_table = self.q_table.append(
                pd.Series(
                    [0]*len(self.actions),
                    index=self.q_table.columns,
                    name=state,
                )
            )

二、Deep Q Network

如果想用Q-learning玩之前的CartPole-v0游戏，会发现CartPole-v0的状态值太多了，它的observation有 车的位置，车的速度，杆子的角度，杆子顶端的速度 四个值，并且是连续的数值，四个值再进行量化，Q表实在是太大了。用Q-learning玩游戏和随机玩游戏没区别，学习不到东西。可能Q-learning只适用于走迷宫类的游戏，每一步的状态都可以很简单的描述出来，4*4的迷宫只需要用16个状态就可以全部囊括。

我们用Deep Q Network来解决这个问题， Deep Q Network融合了神经网络和 Q learning。

我们可以将状态和动作当成神经网络的输入, 然后经过神经网络分析后得到动作的 Q 值, 这样我们就没必要在表格中记录 Q 值, 而是直接使用神经网络生成 Q 值.
或者只输入状态值, 输出所有的动作值, 然后按照 Q learning 的原则, 直接选择拥有最大值的动作当做下一步要做的动作.

需要搭建两个神经网络，target_net 和 eval_net ，
target_net 用于预测 q_target 值, 他不会及时更新参数.
target_net 用于预测 q_eval, 这个神经网络拥有最新的神经网络参数.

两个神经网络结构是完全一样的, 只是里面的参数不一样. target_net 是 eval_net 的一个历史版本, 拥有 eval_net 很久之前的一组参数, 而且这组参数被固定一段时间, 然后再被 eval_net 的新参数所替换. 而 eval_net 是不断在被提升的。这样做是为了打乱数据间的相关性，避免陷入局部最优。

神经网络的输入数据是[s,a,r,s’],输出数据是状态s下所有行为a的Q值。
target_net 只会输出Q值（q_target ），不会进行训练，而eval_net 输出Q值（q_eval）之后会根据q_target和q_eval进行反向传播训练，更新eval_net 的参数。

Deep Q Network整个算法的运作：

初始化target_net 和 target_net。
观察游戏状态observation，选择合适的observation作为输入，一般情况会对observation做数据处理，使其更容易训练，这里不用。
设置合适的奖励reward。
先进行若干次游戏，将游戏数据存储到memory中。
从memory中随机选取训练数据batch_memory用于批量训练。
训练eval_net 一段时间后，将eval_net 的参数复制给target_net 。
训练过程中产生的新的游戏数据会替代memory中的旧数据。

回到游戏CartPole-v0

DQN.py：

import numpy as np
import tensorflow as tf

np.random.seed(1)
tf.set_random_seed(1)


# Deep Q Network off-policy
class DeepQNetwork:
    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,
            output_graph=True,
    ):
        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_]
        # [4, 1, 1, 4]
        self.memory = np.zeros((self.memory_size, n_features * 2 + 2))

        # consist of [target_net, evaluate_net]
        self._build_net()

        t_params = tf.get_collection(tf.GraphKeys.GLOBAL_VARIABLES, scope='target_net')
        e_params = tf.get_collection(tf.GraphKeys.GLOBAL_VARIABLES, scope='eval_net')

        with tf.variable_scope('hard_replacement'):
            self.target_replace_op = [tf.assign(t, e) for t, e in zip(t_params, e_params)]

        self.sess = tf.Session()

        if output_graph:
            # $ tensorboard --logdir=logs
            tf.summary.FileWriter("logs/", self.sess.graph)

        self.sess.run(tf.global_variables_initializer())
        self.cost_his = []

    def _build_net(self):
        # ------------------ all inputs ------------------------
        self.s = tf.placeholder(tf.float32, [None, self.n_features], name='s')  # input State
        self.s_ = tf.placeholder(tf.float32, [None, self.n_features], name='s_')  # input Next State
        self.r = tf.placeholder(tf.float32, [None, ], name='r')  # input Reward
        self.a = tf.placeholder(tf.int32, [None, ], name='a')  # input Action

        w_initializer, b_initializer = tf.random_normal_initializer(0., 0.3), tf.constant_initializer(0.1)

        # ------------------ build evaluate_net ------------------
        with tf.variable_scope('eval_net'):
            e1 = tf.layers.dense(self.s, 20, tf.nn.relu, kernel_initializer=w_initializer,
                                 bias_initializer=b_initializer, name='e1')
            self.q_eval = tf.layers.dense(e1, self.n_actions, kernel_initializer=w_initializer,
                                          bias_initializer=b_initializer, name='q')

        # ------------------ build target_net ------------------
        with tf.variable_scope('target_net'):
            t1 = tf.layers.dense(self.s_, 20, tf.nn.relu, kernel_initializer=w_initializer,
                                 bias_initializer=b_initializer, name='t1')
            self.q_next = tf.layers.dense(t1, self.n_actions, kernel_initializer=w_initializer,
                                          bias_initializer=b_initializer, name='t2')

        with tf.variable_scope('q_target'):
            q_target = self.r + self.gamma * tf.reduce_max(self.q_next, axis=1, name='Qmax_s_')  # shape=(None, )
            self.q_target = tf.stop_gradient(q_target)
        with tf.variable_scope('q_eval'):
            a_indices = tf.stack([tf.range(tf.shape(self.a)[0], dtype=tf.int32), self.a], axis=1)
            self.q_eval_wrt_a = tf.gather_nd(params=self.q_eval, indices=a_indices)  # shape=(None, )
        with tf.variable_scope('loss'):
            self.loss = tf.reduce_mean(tf.squared_difference(self.q_target, self.q_eval_wrt_a, name='TD_error'))
        with tf.variable_scope('train'):
            self._train_op = tf.train.RMSPropOptimizer(self.lr).minimize(self.loss)

    def store_transition(self, s, a, r, s_):
        if not hasattr(self, 'memory_counter'):
            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[index, :] = transition
        self.memory_counter += 1

    def choose_action(self, observation):
        # to have batch dimension when feed into tf placeholder
        observation = observation[np.newaxis, :]

        if np.random.uniform() < self.epsilon:
            # forward feed the observation and get q value for every actions
            actions_value = self.sess.run(self.q_eval, feed_dict={ 
   self.s: observation})
            action = np.argmax(actions_value)
        else:
            action = np.random.randint(0, self.n_actions)
        return action

    def learn(self):
        # check to replace target parameters
        if self.learn_step_counter % self.replace_target_iter == 0:
            self.sess.run(self.target_replace_op)
            print('\ntarget_params_replaced\n')

        # sample batch memory from all memory
        if self.memory_counter > self.memory_size:
            sample_index = np.random.choice(self.memory_size, size=self.batch_size)
        else:
            sample_index = np.random.choice(self.memory_counter, size=self.batch_size)
        batch_memory = self.memory[sample_index, :]

        _, cost = self.sess.run(
            [self._train_op, self.loss],
            feed_dict={ 
   
                self.s: batch_memory[:, :self.n_features],
                self.a: batch_memory[:, self.n_features],
                self.r: batch_memory[:, self.n_features + 1],
                self.s_: batch_memory[:, -self.n_features:],
            })

        self.cost_his.append(cost)

        # 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):
        import matplotlib.pyplot as plt
        plt.plot(np.arange(len(self.cost_his)), self.cost_his)
        plt.ylabel('Cost')
        plt.xlabel('training steps')
        plt.show()


if __name__ == '__main__':
    DQN = DeepQNetwork(3, 4, output_graph=True)

DQN_CarPole.py:

import gym
from DQN import DeepQNetwork

env = gym.make('CartPole-v0')
env = env.unwrapped
RL = DeepQNetwork(n_actions=env.action_space.n,
                  n_features=env.observation_space.shape[0],
                  learning_rate=0.01, e_greedy=0.9,
                  replace_target_iter=100, memory_size=2000,
                  e_greedy_increment=0.0008, )
total_steps = 0  # 记录步数

for i_episode in range(100):

    # 获取回合 i_episode 第一个 observation
    observation = env.reset()
    ep_r = 0
    while True:
        env.render()  # 刷新环境

        action = RL.choose_action(observation)  # 选行为

        observation_, reward, done, info = env.step(action)  # 获取下一个 state

        x, x_dot, theta, theta_dot = observation_  # 细分开, 为了修改原配的 reward

        # x 是车的水平位移, 所以 r1 是车越偏离中心, 分越少
        # theta 是棒子离垂直的角度, 角度越大, 越不垂直. 所以 r2 是棒越垂直, 分越高
        r1 = (env.x_threshold - abs(x)) / env.x_threshold - 0.8
        r2 = (env.theta_threshold_radians - abs(theta)) / env.theta_threshold_radians - 0.5
        reward = r1 + r2  # 总 reward 是 r1 和 r2 的结合, 既考虑位置, 也考虑角度, 这样 DQN 学习更有效率

        # 保存这一组记忆
        RL.store_transition(observation, action, reward, observation_)

        if total_steps > 1000:
            RL.learn()  # 学习

        ep_r += reward
        if done:
            print('episode: ', i_episode,
                  'ep_r: ', round(ep_r, 2),
                  ' epsilon: ', round(RL.epsilon, 2))
            break

        observation = observation_
        total_steps += 1
# 最后输出 cost 曲线
RL.plot_cost()
env.close()

运行DQN_CarPole.py
发现小车确实变得越来越稳定。

最后输出的损失函数曲线
在这里插入图片描述

三、Double DQN

无论是Q-learning还是DQN，更新Q值的的时候都会用到 $m a x Q$ 。

Q-learning:
$Q(s,a)←Q(s,a)+α[r+\gamma max_{a'}Q(s^′,a^′)−Q(s,a)]$

DQN:
在这里插入图片描述

使用max虽然可以快速让Q值向可能的优化目标靠拢，但是很容易过犹不及，导致过度估计(Over Estimation)，所谓过度估计就是最终我们得到的算法模型有很大的偏差(bias)，可能就会发现Q值都超级大。

DDQN通过解耦目标Q值动作的选择和目标Q值的计算这两步，来达到消除过度估计的问题。

在这里插入图片描述
DDQN更新：

在DDQN这里，不再是直接在目标Q网络里面找各个动作中最大Q值，而是先在当前Q网络中先找出最大Q值对应的动作。然后利用这个选择出来的动作在目标Q网络里面去计算目标Q值。

DoubleDQN.py

import numpy as np
import tensorflow as tf

np.random.seed(1)
tf.set_random_seed(1)


class DoubleDQN:
    def __init__(
            self,
            n_actions,
            n_features,
            learning_rate=0.005,
            reward_decay=0.9,
            e_greedy=0.9,
            replace_target_iter=200,
            memory_size=3000,
            batch_size=32,
            e_greedy_increment=None,
            output_graph=False,
    ):
        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
        self.learn_step_counter = 0
        self.memory = np.zeros((self.memory_size, n_features * 2 + 2))
        self._build_net()
        t_params = tf.get_collection('target_net_params')
        e_params = tf.get_collection('eval_net_params')
        self.replace_target_op = [tf.assign(t, e) for t, e in zip(t_params, e_params)]

        self.sess = tf.Session()

        if output_graph:
            tf.summary.FileWriter("logs/", self.sess.graph)

        self.sess.run(tf.global_variables_initializer())
        self.cost_his = []

    def _build_net(self):
        def build_layers(s, c_names, n_l1, w_initializer, b_initializer):
            with tf.variable_scope('l1'):
                w1 = tf.get_variable('w1', [self.n_features, n_l1], initializer=w_initializer, collections=c_names)
                b1 = tf.get_variable('b1', [1, n_l1], initializer=b_initializer, collections=c_names)
                l1 = tf.nn.relu(tf.matmul(s, w1) + b1)

            with tf.variable_scope('l2'):
                w2 = tf.get_variable('w2', [n_l1, self.n_actions], initializer=w_initializer, collections=c_names)
                b2 = tf.get_variable('b2', [1, self.n_actions], initializer=b_initializer, collections=c_names)
                out = tf.matmul(l1, w2) + b2
            return out

        # ------------------ build evaluate_net ------------------
        self.s = tf.placeholder(tf.float32, [None, self.n_features], name='s')  # input
        self.q_target = tf.placeholder(tf.float32, [None, self.n_actions], name='Q_target')  # for calculating loss

        with tf.variable_scope('eval_net'):
            c_names, n_l1, w_initializer, b_initializer = \
                ['eval_net_params', tf.GraphKeys.GLOBAL_VARIABLES], 20, \
                tf.random_normal_initializer(0., 0.3), tf.constant_initializer(0.1)  # config of layers

            self.q_eval = build_layers(self.s, c_names, n_l1, w_initializer, b_initializer)

        with tf.variable_scope('loss'):
            self.loss = tf.reduce_mean(tf.squared_difference(self.q_target, self.q_eval))
        with tf.variable_scope('train'):
            self._train_op = tf.train.RMSPropOptimizer(self.lr).minimize(self.loss)

        # ------------------ build target_net ------------------
        self.s_ = tf.placeholder(tf.float32, [None, self.n_features], name='s_')  # input
        with tf.variable_scope('target_net'):
            c_names = ['target_net_params', tf.GraphKeys.GLOBAL_VARIABLES]

            self.q_next = build_layers(self.s_, c_names, n_l1, w_initializer, b_initializer)

    def store_transition(self, s, a, r, s_):
        if not hasattr(self, 'memory_counter'):
            self.memory_counter = 0
        transition = np.hstack((s, [a, r], s_))
        index = self.memory_counter % self.memory_size
        self.memory[index, :] = transition
        self.memory_counter += 1

    def choose_action(self, observation):
        observation = observation[np.newaxis, :]
        actions_value = self.sess.run(self.q_eval, feed_dict={ 
   self.s: observation})
        action = np.argmax(actions_value)

        if not hasattr(self, 'q'):  # record action value it gets
            self.q = []
            self.running_q = 0
        self.running_q = self.running_q * 0.99 + 0.01 * np.max(actions_value)
        self.q.append(self.running_q)

        if np.random.uniform() > self.epsilon:  # choosing action
            action = np.random.randint(0, self.n_actions)
        return action

    def learn(self):
        if self.learn_step_counter % self.replace_target_iter == 0:
            self.sess.run(self.replace_target_op)
            print('\ntarget_params_replaced\n')

        if self.memory_counter > self.memory_size:
            sample_index = np.random.choice(self.memory_size, size=self.batch_size)
        else:
            sample_index = np.random.choice(self.memory_counter, size=self.batch_size)
        batch_memory = self.memory[sample_index, :]

        q_next, q_eval4next = self.sess.run(
            [self.q_next, self.q_eval],
            feed_dict={ 
   self.s_: batch_memory[:, -self.n_features:],  # next observation
                       self.s: batch_memory[:, -self.n_features:]})  # next observation
        q_eval = self.sess.run(self.q_eval, { 
   self.s: batch_memory[:, :self.n_features]})

        q_target = q_eval.copy()

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

        max_act4next = np.argmax(q_eval4next,
                                 axis=1)  # the action that brings the highest value is evaluated by q_eval
        selected_q_next = q_next[batch_index, max_act4next]  # Double DQN, select q_next depending on above actions

        q_target[batch_index, eval_act_index] = reward + self.gamma * selected_q_next

        _, self.cost = self.sess.run([self._train_op, self.loss],
                                     feed_dict={ 
   self.s: batch_memory[:, :self.n_features],
                                                self.q_target: q_target})
        self.cost_his.append(self.cost)

        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):
        import matplotlib.pyplot as plt
        plt.plot(np.arange(len(self.cost_his)), self.cost_his)
        plt.ylabel('Cost')
        plt.xlabel('training steps')
        plt.show()

DoubleDQN_CarPole.py

import tensorflow as tf
import gym
from DoubleDQN import DoubleDQN

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

double_DQN = DoubleDQN(n_actions=env.action_space.n,
                       n_features=env.observation_space.shape[0],
                       memory_size=2000,
                       e_greedy_increment=0.001,
                       output_graph=True)
total_steps = 0  # 记录步数

for i_episode in range(100):

    # 获取回合 i_episode 第一个 observation
    observation = env.reset()
    ep_r = 0
    while True:
        env.render()  # 刷新环境

        action = double_DQN.choose_action(observation)  # 选行为

        observation_, reward, done, info = env.step(action)  # 获取下一个 state

        x, x_dot, theta, theta_dot = observation_  # 细分开, 为了修改原配的 reward

        # x 是车的水平位移, 所以 r1 是车越偏离中心, 分越少
        # theta 是棒子离垂直的角度, 角度越大, 越不垂直. 所以 r2 是棒越垂直, 分越高
        r1 = (env.x_threshold - abs(x)) / env.x_threshold - 0.8
        r2 = (env.theta_threshold_radians - abs(theta)) / env.theta_threshold_radians - 0.5
        reward = r1 + r2  # 总 reward 是 r1 和 r2 的结合, 既考虑位置, 也考虑角度, 这样 DQN 学习更有效率

        # 保存这一组记忆
        double_DQN.store_transition(observation, action, reward, observation_)

        if total_steps > 1000:
            double_DQN.learn()  # 学习

        ep_r += reward
        if done:
            print('episode: ', i_episode,
                  'ep_r: ', round(ep_r, 2),
                  ' epsilon: ', round(double_DQN.epsilon, 2))
            break

        observation = observation_
        total_steps += 1
# 最后输出 cost 曲线
double_DQN.plot_cost()
env.close()

输出损失函数结果
在这里插入图片描述
对比DQN，可以发现DoubleDQN效果明显好很多。

版权说明 : 本文为转载文章, 版权为原作者所有

原文标题 : 深度强化学习（DRL）三：从Q-learning到Deep Q Network(DQN)

原文连接 : https://blog.csdn.net/windowsyun/article/details/104564888

目录

一、Q-learning

二、Deep Q Network

三、Double DQN

主题目录