一、Q-Learning算法

Q-Learning算法中动作值函数Q的更新方向是最优动作值函数q，而与Agent所遵循的行为策略无关，在评估动作值函数Q时，更新目标为最优动作值函数q的直接近似，故需要遍历当前状态的所有动作，在所有状态都能被无限次访问的前提下，Q-Learning算法能以1的概率收敛到最优动作值函数和最优策略

下图是估算最优策略的Q-Learning算法流程图

Q-Learning虽然是异策略，但是从值函数更新迭代式中可以看出，它并没有使用到重要性采样。

使用Q-Learning算法解决确定环境中的扫地机器人问题参数设置与之前相同使用贪心策略

机器人背景及环境搭建

输出如下

代码如下


#Q-learning算法
from 扫地机器人gym环境 import GridWorldEnv
import numpy as np
np.random.seed(1)
env = GridWorldEnv()
#有效动作空间
def vilid_action_space(s):
    action_sacpe = []
    if s % 5 != 0:#左
        action_sacpe.append(0)
    if s % 5 != 4:#右
        action_sacpe.append(1)
    if s <= 19:#上
        action_sacpe.append(2)
    if s >= 5:#下
        action_sacpe.append(3)
    return action_sacpe

def policy_epsilon_greedy(s, Q, epsilon):
    Q_s = Q[s]
    action = vilid_action_space(s)
    if np.random.rand() < epsilon:
        a = np.random.choice(action)
    else:
        index_a = np.argmax([Q_s[i] for i in action])
        a = action[index_a]
    return a

def trans1(Q_S):
    new_Q = []
    new_Q.append(Q_S[2])
    new_Q.append(Q_S[3])
    new_Q.append(Q_S[0])
    new_Q.append(Q_S[1])
    return new_Q

def trans(Q_S):
    new_Q = []
    new_Q.append(round(Q_S[2],3))
    new_Q.append(round(Q_S[3],3))
    new_Q.append(round(Q_S[0],3))
    new_Q.append(round(Q_S[1],3))
    return new_Q

def print_dd(s, a, next_s, print_len, episode_i, Q,e_k,a_k):
    for i in range(2):
        if episode_i == int(print_len * (0.1 * i + 1)):
            if s == 15 and a == 3 and next_s == 10:
                print("*********************************单步的计算过程***************************************")
                print("alpha:"+str(a_k))
                print("epsilon:"+str(e_k))
                print("state:" + str(int(print_len * (0.1 * i + 1))))
                print("Q(%d,%d)"%(s,a))
                print(Q[s][a])
                print("Q(%d,*)"%(next_s))
                print(trans1(Q[next_s]))
                print('output:'+str(Q[s][a] + a_k * (0.8 * np.max(Q[next_s]) - Q[s, a])))

def print_ff(list_q, Q, episode_i,epsilon_k,alpha_k):
    list_s = range(0,25)
    for em in list_q:
        if em == episode_i:
            print("*******************************情节数:%s*******************************"%(str(em)))
            for state in list_s:
                print("Q(%d,*)"%(state) + str(trans(Q[state])))
                action = vilid_action_space(state)
                len_a = len(action)
                e_p = epsilon_k / float(len_a)
                max_a = np.argmax(Q[state])
                prob = []
                index_a = np.argmax([Q[state][i] for i in action])
                for i in range(4):#计算epsilon
                    if i not in action:
                        prob.append(0.0)
                    else:
                        if i == action[index_a]:
                            prob.append(1 - epsilon_k + e_p)
                        else:
                            prob.append(e_p)
                print('概率值:' + str(trans(prob)))
                print("epsilon_k: {}".format(epsilon_k))
                print("alpha_k:{}".format(alpha_k))

def Attenuation(epsilon,alpha,episode_sum,episode):
    epsilon = (float(episode_sum) - float(episode)) / float(episode_sum) * epsilon
    alpha = (float(episode_sum) - float(episode)) / float(episode_sum) * alpha
    return epsilon, alpha

        while not done:
            a = policy_epsilon_greedy(s, Q, epsilon_k)
            next_s, r, done, _ = env.step(a)
            print_dd(s, a, next_s, 10000, episode_i, Q, epsilon_k, alpha_k)
            Q[s, a] += alpha_k * (r + gamma * np.max(Q[next_s]) - Q[s, a])
            s = next_s
    return Q

Q = Q_Learning(env, 25000, 0.05, 0.8, 0.5)

二、期望Sarsa算法

通过对Sarsa算法进行改进，得到一种异策略TD算法，该算法考虑当前策略下所有动作的可能性，利用动作值函数的期望值取代某一特定动作值函数来更新估计值，该算法称为期望Sarsa算法。

相比于Sarsa算法，期望Sarsa算法计算更为复杂，但通过计算能够有效地消除银随机选择而产生的方差，因此通常情况下，期望Sarsa算法明显优于Sarsa算法，另外期望Sarsa算法还可以使用异策略方法，将Q-Learning进行推广并提升性能

下面利用期望Sarsa算法解决确定环境扫地机器人问题背景与前面相同不再赘述

迭代到20000次后基本Q值已经收敛

代码如下


# 期望Sarsa算法
from 扫地机器人gym环境 import GridWorldEnv
import numpy as np
from queue import Queue

np.random.seed(1)
env = GridWorldEnv()


# 有效动作空间
def vilid_action_space(s):
    action_sacpe = []
    if s % 5 != 0:  # 左
        action_sacpe.append(0)
    if s % 5 != 4:  # 右
        action_sacpe.append(1)
    if s <= 19:  # 上
        action_sacpe.append(2)
    if s >= 5:  # 下
        action_sacpe.append(3)
    return action_sacpe


def policy_epsilon_greedy(s, Q, epsilon):
    Q_s = Q[s]
    action = vilid_action_space(s)
    if np.random.rand() < epsilon:
        a = np.random.choice(action)
    else:
        index_a = np.argmax([Q_s[i] for i in action])
        a = action[index_a]
    return a


def compute_epsion(s, Q, epsilon):
    max_a = np.argmax(Q[s])
    action = vilid_action_space(s)
    len_all_a = len(action)
    prob_l = [0.0, 0.0, 0.0, 0.0]
    for index_a in action:
        if index_a == max_a:
            prob_l[index_a] = 1.0 - epsilon + (epsilon / len_all_a)
        else:
            prob_l[index_a] = epsilon / len_all_a
    return prob_l


def compute_e_q(prob, q_n):
    sum = 0.0
    for i in range(4):
        sum += prob[i] * q_n[i]
    return sum


def trans1(Q_S):
    new_Q = []
    new_Q.append(Q_S[2])
    new_Q.append(Q_S[3])
    new_Q.append(Q_S[0])
    new_Q.append(Q_S[1])
    return new_Q


def print_dd(s, a, next_s, print_len, episode_i, Q, e_k, a_k):
    for i in range(50):
        if episode_i == int(print_len * ((0.02 * i) + 1)):
            if s == 15 and a == 3 and next_s == 10:
                print("*****************************单步计算过程****************************************")
                print("alpha:" + str(a_k))
                print("epsilon:" + str(e_k))
                print("state:" + str(int(print_len * (1 + (0.02 * i)))))
                print("Q(%d,%d)" % (s, a))
                print(Q[s][a])
                print("Q(%d,*)" % (next_s))
                print(trans1(Q[next_s]))
                prob_l = compute_epsion(next_s, Q, e_k)
                print('概率' + str(trans1(prob_l)))
                Q_e = compute_e_q(prob_l, Q[next_s])
                print('update:' + str(Q[s, a] + a_k * (0.8 * Q_e - Q[s, a])))


def trans(Q_S):
    new_Q = []
    new_Q.append(round(Q_S[2], 3))
    new_Q.append(round(Q_S[3], 3))
    new_Q.append(round(Q_S[0], 3))
    new_Q.append(round(Q_S[1], 3))
    return new_Q


def print_ff(list_q, Q, episode_i, epsilon_k, alpha_k):
    list_s = range(0, 25)
    for em in list_q:
        if em == episode_i:
            print("*******************************情节数:%s*******************************" % (str(em)))
            for state in list_s:
                print("Q(%d,*) " % (state) + str(trans(Q[state])))
                action = vilid_action_space(state)
                len_a = len(action)
                e_p = epsilon_k / float(len_a)
                prob = []
                index_a = np.argmax([Q[state][i] for i in action])
                for i in range(4):  # 计算epsilon
                    if i not in action:
                        prob.append(0.0)
                    else:
                        if i == action[index_a]:
                            prob.append(1 - epsilon_k + e_p)
                        else:
                            prob.append(e_p)
                print('概率值:' + str(trans(prob)))
                print("epsilon_k: {}".format(epsilon_k))
                print("alpha_k:{}".format(alpha_k))


def Attenuation(epsilon, alpha, episode_sum, episode):
    epsilon = (float(episode_sum) - float(episode)) / float(episode_sum) * epsilon
    alpha = (float(episode_sum) - float(episode)) / float(episode_sum) * alpha
    return epsilon, alpha


def Expectation_sarsa(env, episode_num, alpha, gamma, epsilon):
    Q = np.zeros((env.n_width * env.n_height, env.action_space.n))
    Q_queue = Queue(maxsize=11)
lon_k, alpha_k)
            prob_l = compute_epsion(next_s, Q, epsilon_k)
            Q_e = compute_e_q(prob_l, Q[next_s])
            Q[s, a] += alpha_k * (r + gamma * Q_e - Q[s, a])
            s = next_s
    return Q


Q = Expectation_sarsa(env, 20000, 0.05, 0.8, 0.5)

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