基础知识

关于Q-learning 和 Sarsa 算法, 详情参见博客 强化学习（Q-Learning，Sarsa）
Sarsa 算法框架为
Q-learning 算法框架为

关于FrozenLake-v0环境介绍, 请参见https://copyfuture.com/blogs-details/20200320113725944awqrghbojzsr9ce

此图来自 强化学习FrozenLake求解

需要注意的细节

训练时

• 采用 $ϵ$ 贪心算法;

# 贪婪动作选择，含嗓声干扰
a = np.argmax(Q_all[s, :] + np.random.randn(1, env.action_space.n) * (1. / (i + 1)))

• 对 Q-learning 算法

# 更新Q表
# Q-learning
Q_all[s, a] = Q_all[s, a] + alpha * (r + gamma * np.max(Q_all[s1, :]) - Q_all[s, a])

• 对 Sarsa 算法

# sarsa
# 更新Q表
a_ = np.argmax(Q_all[s1, :] + np.random.randn(1, env.action_space.n) * (1. / (i + 1)))
Q_all[s, a] = Q_all[s, a] + alpha * (r + gamma * Q_all[s1, a_] - Q_all[s, a])

测试时

• 不采用 $ϵ$ 贪心算法;

a = np.argmax(Q_all[s, :])

• 不更新Q表

# # 不更新Q表
# Q_all[s, a] = Q_all[s, a] + alpha * (r + gamma * np.max(Q_all[s1, :]) - Q_all[s, a])

寻找模型中最优的$\alpha$, $\gamma$

我们计算一下不同参数下的学习率， 如下图所示


比较两种算法的准确率, 我们用Q-learning算法的准确率减掉Sarsa的准确率, 得到

从图中可以看到, 大于0的点均表明在此点对应的$\alpha ,\gamma$下, Q-learning 准确率高于Sarsa.

Python代码

import gym
import numpy as np
import random
import matplotlib.pyplot as plt
from mpl_toolkits.axes_grid1 import make_axes_locatable

# gym创建冰湖环境
env = gym.make('FrozenLake-v0')
env.render()  # 显示初始environment
# 初始化Q表格，矩阵维度为【S,A】，即状态数*动作数
Q_all = np.zeros([env.observation_space.n, env.action_space.n])
# 设置参数,
# 其中α\alpha 为学习速率（learning rate），γ\gamma为折扣因子（discount factor）
alpha = 0.8
gamma = 0.95
num_episodes = 2000
#
Alpha = np.arange(0.75, 1, 0.02)
Gamma = np.arange(0.1, 1, 0.05)
#Alpha = np.ones_like(Gamma)*0.97
# Training
correct_train = np.zeros([len(Alpha), len(Gamma)])
correct_test = np.zeros([len(Alpha), len(Gamma)])
for k in range(len(Alpha)):
    for p in range(len(Gamma)):
        alpha = Alpha[k]
        gamma = Gamma[p]

        # training
        rList = []
        for i in range(num_episodes):
            # 初始化环境，并开始观察

            s = env.reset()
            rAll = 0
            d = False
            j = 0
            # 最大步数
            while j < 99:
                j += 1
                # 贪婪动作选择，含嗓声干扰
                a = np.argmax(Q_all[s, :] + np.random.randn(1, env.action_space.n) * (1. / (i + 1)))

                # 从环境中得到新的状态和回报
                s1, r, d, _ = env.step(a)
                # 更新Q表
                # Q-learning
                Q_all[s, a] = Q_all[s, a] + alpha * (r + gamma * np.max(Q_all[s1, :]) - Q_all[s, a])
                # sarsa
                a_ = np.argmax(Q_all[s1, :] + np.random.randn(1, env.action_space.n) * (1. / (i + 1)))
                Q_all[s, a] = Q_all[s, a] + alpha * (r + gamma * Q_all[s1, a_] - Q_all[s, a])
                # 累加回报
                rAll += r
                # 更新状态
                s = s1
                # Game Over
                if d:
                    break
            rList.append(rAll)
        correct_train[k, p] = (sum(rList) / num_episodes)
        # test
        rList = []
        for i in range(num_episodes):
            # 初始化环境，并开始观察
            s = env.reset()
            rAll = 0
            d = False
            j = 0
            # 最大步数
            while j < 99:
                j += 1
                # 贪婪动作选择，含嗓声干扰
                a = np.argmax(Q_all[s, :])
                # 从环境中得到新的状态和回报
                s1, r, d, _ = env.step(a)
                # # 更新Q表
                # Q_all[s, a] = Q_all[s, a] + alpha * (r + gamma * np.max(Q_all[s1, :]) - Q_all[s, a])
                # 累加回报
                rAll += r
                # 更新状态
                s = s1
                # Game Over
                if d:
                    break
            rList.append(rAll)
        correct_test[k, p] = sum(rList) / num_episodes

# print("Score over time：" + str(sum(rList) / num_episodes))
# print("打印Q表：", Q_all)

# Test
plt.figure()
ax = plt.subplot(1, 1, 1)
h = plt.imshow(correct_train, interpolation='nearest', cmap='rainbow',
               extent=[0.75, 1, 0, 1],
               origin='lower', aspect='auto')
divider = make_axes_locatable(ax)
cax = divider.append_axes("right", size="5%", pad=0.05)
plt.colorbar(h, cax=cax)
plt.show()

参考文献

【1】https://blog.csdn.net/kyolxs/article/details/86693085
【2】 强化学习（Q-Learning，Sarsa）
【3】 强化学习FrozenLake求解
【4】https://copyfuture.com/blogs-details/20200320113725944awqrghbojzsr9ce