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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 GridWorldEnvimport numpy as npnp.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_sacpedef 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 adef 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_Qdef 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_Qdef 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epsilonif 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) * epsilonalpha = (float(episode_sum) - float(episode)) / float(episode_sum) * alphareturn epsilon, alphawhile 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_sreturn QQ = 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 GridWorldEnvimport numpy as npfrom queue import Queuenp.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_sacpedef 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 adef 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_areturn prob_ldef compute_e_q(prob, q_n):sum = 0.0for i in range(4):sum += prob[i] * q_n[i]return sumdef 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_Qdef 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_Qdef 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epsilonif 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) * epsilonalpha = (float(episode_sum) - float(episode)) / float(episode_sum) * alphareturn epsilon, alphadef 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_sreturn QQ = Expectation_sarsa(env, 20000, 0.05, 0.8, 0.5)

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