Double DQN原理

DQN本质上仍然是Q-learning，只是利用了神经网络表示动作值函数，并利用了经验回放和单独设立目标网络这两个技巧。DQN无法克服Q-learning 本身所固有的缺点——过估计。过估计是指估计的值函数比真实值函数要大。一般来说，Q-learning之所以存在过估计的问题，根源在于Q-learning中的最大化操作。

DQN

Max操作使得估计的值函数比值函数的真实值大。如果值函数每一点的值都被过估计了相同的幅度，即过估计量是均匀的，那么由于最优策略是贪婪策略，即找到最大的值函数所对应的动作，这时候最优策略是保持不变的。也就是说，在这种情况下，即使值函数被过估计了，也不影响最优的策略。强化学习的目标是找到最优的策略，而不是要得到值函数，所以这时候就算是值函数被过估计了，最终也不影响我们解决问题。然而，在实际情况中，过估计量并非是均匀的，因此值函数的过估计会影响最终的策略决策，从而导致最终的策略并非最优，而只是次优。

为了解决值函数过估计的问题，Double Q-learning 将动作的选择和动作的评估分别用不同的值函数来实现。

Paper：
DDQN:Deep Reinforcement Learning with Double Q-learning

Github：https://github.com/xiaochus/Deep-Reinforcement-Learning-Practice

环境

• Python 3.6
• Tensorflow-gpu 1.8.0
• Keras 2.2.2
• Gym 0.10.8

算法实现

Double DQN和Nature DQN的区别仅仅在于目标Q值的计算。

在之前的文章中，Nature DQN中的target_Q是这样计算的：

        y = self.model.predict(states)
        q = self.target_model.predict(next_states)

        for i, (_, action, reward, _, done) in enumerate(data):
            target = reward
            if not done:
                target += self.gamma * np.amax(q[i])
            y[i][action] = target

在Double DQN中，target_Q是这样计算的：

        y = self.model.predict(states)
        q = self.target_model.predict(next_states)
        next_action = np.argmax(self.model.predict(next_states), axis=1)

        for i, (_, action, reward, _, done) in enumerate(data):
            target = reward
            if not done:
                target += self.gamma * q[i][next_action[i]]
            y[i][action] = target

两者的区别在于，在对next时刻的Q值进行选取时，不在使用最大值，而是使用主网络预测出来的next_action进行选取，除此之外算法其余部分完全一样。

完整代码：

# -*- coding: utf-8 -*-
import os
import random
import numpy as np

from DQN import DQN


class DDQN(DQN):
    """Nature Deep Q-Learning.
    """
    def __init__(self):
        super(DDQN, self).__init__()

        self.model = self.build_model()
        self.target_model = self.build_model()
        self.update_target_model()

        if os.path.exists('model/ddqn.h5'):
            self.model.load_weights('model/ddqn.h5')

    def update_target_model(self):
        """update target_model
        """
        self.target_model.set_weights(self.model.get_weights())

    def process_batch(self, batch):
        """process batch data
        Arguments:
            batch: batch size

        Returns:
            X: states
            y: [Q_value1, Q_value2]
        """
         # ranchom choice batch data from experience replay.
        data = random.sample(self.memory_buffer, batch)
        # Q_target。
        states = np.array([d[0] for d in data])
        next_states = np.array([d[3] for d in data])

        y = self.model.predict(states)
        q = self.target_model.predict(next_states)
        next_action = np.argmax(self.model.predict(next_states), axis=1)

        for i, (_, action, reward, _, done) in enumerate(data):
            target = reward
            if not done:
                target += self.gamma * q[i][next_action[i]]
            y[i][action] = target

        return states, y

    def train(self, episode, batch):
        """training 
        Arguments:
            episode: game episode
            batch： batch size

        Returns:
            history: training history
        """
        history = {'episode': [], 'Episode_reward': [], 'Loss': []}

        count = 0
        for i in range(episode):
            observation = self.env.reset()
            reward_sum = 0
            loss = np.infty
            done = False

            while not done:
                # chocie action from ε-greedy.
                x = observation.reshape(-1, 4)
                action = self.egreedy_action(x)
                observation, reward, done, _ = self.env.step(action)
                # add data to experience replay.
                reward_sum += reward
                self.remember(x[0], action, reward, observation, done)

                if len(self.memory_buffer) > batch:
                    X, y = self.process_batch(batch)
                    loss = self.model.train_on_batch(X, y)

                    count += 1
                    # reduce epsilon pure batch.
                    self.update_epsilon()

                    # update target_model every 20 episode
                    if count != 0 and count % 20 == 0:
                        self.update_target_model()

            if i % 5 == 0:
                history['episode'].append(i)
                history['Episode_reward'].append(reward_sum)
                history['Loss'].append(loss)

                print('Episode: {} | Episode reward: {} | loss: {:.3f} | e:{:.2f}'.format(i, reward_sum, loss, self.epsilon))

        self.model.save_weights('model/ddqn.h5')

        return history


if __name__ == '__main__':
    model = DDQN()

    history = model.train(600, 32)
    model.save_history(history, 'ddqn.csv')

    model.play('dqn')

训练与测试结果如下，在使用与DQN同样的参数的情况下，可以看出Double DQN收敛的更好，在每次测试中都能够拿到200的分数。

Episode: 550 | Episode reward: 143.0 | loss: 0.052 | e:0.01
Episode: 555 | Episode reward: 200.0 | loss: 0.010 | e:0.01
Episode: 560 | Episode reward: 200.0 | loss: 0.750 | e:0.01
Episode: 565 | Episode reward: 157.0 | loss: 0.067 | e:0.01
Episode: 570 | Episode reward: 200.0 | loss: 0.018 | e:0.01
Episode: 575 | Episode reward: 200.0 | loss: 5.615 | e:0.01
Episode: 580 | Episode reward: 200.0 | loss: 0.035 | e:0.01
Episode: 585 | Episode reward: 200.0 | loss: 0.011 | e:0.01
Episode: 590 | Episode reward: 200.0 | loss: 0.041 | e:0.01
Episode: 595 | Episode reward: 156.0 | loss: 6.012 | e:0.01
play...
Reward for this episode was: 200.0
Reward for this episode was: 200.0
Reward for this episode was: 200.0
Reward for this episode was: 200.0
Reward for this episode was: 200.0
Reward for this episode was: 200.0
Reward for this episode was: 200.0
Reward for this episode was: 200.0
Reward for this episode was: 200.0
Reward for this episode was: 200.0

DDQN

CMP