强化学习之价值迭代算法动态规划求解悬崖漫步环境（CliffWalking）最优策略及最优状态价值函数

class CliffWalkingEnv:def __init__(self,ncol=12,nrow=4):self.ncol=ncol#定义网格世界的列self.nrow=nrow#定义网格世界的行self.P=self.createP()#转移矩阵P[state][action]=[(p,next_state,reward,done)]包含下一个状态和奖励def createP(self):P=[[[]for i in range(4)]for j in range(self.ncol*self.nrow)]#初始化change=[[0,-1],[0,1],[-1,0],[1,0]]#4种动作，change[0]:上;change[0]:上;change[0]:上;change[0]:上。[列变化，行变化]；坐标系原点(0,0)for i in range(self.nrow):for j in range(self.ncol):for a in range(len(change)):if i==self.nrow-1 and j>0:#如果在悬崖或者目标状态，任何动作奖励都为0P[i*self.ncol+j][a]=[(1,i*self.ncol+j,0,True)]continuenext_x=min(self.ncol-1,max(0,j+change[a][0]))next_y=min(self.nrow-1,max(0,i+change[a][1]))next_state=next_y*self.ncol+next_xreward=-1done=Falseif next_y==self.ncol-1 and next_x>0:#如果下一个位置在悬崖或者终点，done=Truedone=Trueif next_x==self.ncol:#如果在悬崖，奖励为-100reward=-100P[i*self.ncol+j][a]=[(1,next_state,reward,done)]return P
class ValueIteration:""" 价值迭代算法 """def __init__(self,env,theta,gamma):self.env=envself.theta=theta#策略评估收敛阈值self.gamma=gamma#折扣因子self.v=[0]*(self.env.ncol*self.env.nrow)#初始化价值为0self.pi=[None for i in range(self.env.ncol*self.env.nrow)]def value_iteration(self):count=0while 1:max_diff=0new_v=[0]*self.env.ncol*self.env.nrowfor s in range(self.env.ncol*self.env.nrow):Qsa_list=[]#开始计算状态s下面的所有Q(s,a)价值for a in range(4):Qsa=0for res in self.env.P[s][a]:p,next_state,reward,done=resQsa+=p*(reward+self.gamma*self.v[next_state]*(1-done))Qsa_list.append(Qsa)new_v[s]=max(Qsa_list)max_diff=max(max_diff,abs(new_v[s]-self.v[s]))self.v=new_vif max_diff<self.theta:breakcount+=1print("价值迭代进行%d轮后完成"%count)self.getpolicy()def getpolicy(self):#价值迭代完成后，根据价值函数导出一个贪婪策略for s in range(self.env.ncol*self.env.nrow):Qsa_list=[]for a in range(4):Qsa=0for res in self.env.P[s][a]:p,next_state,reward,done=resQsa+=p*(reward+self.gamma*self.v[next_state]*(1-done))Qsa_list.append(Qsa)max_Qsa=max(Qsa_list)count_max_Qsa=Qsa_list.count(max_Qsa)self.pi[s]=[1/count_max_Qsa if p==max_Qsa else 0 for p in Qsa_list]
def print_agent(agent,action_meaning,disater=[],end=[]):print("状态价值：")for i in range(agent.env.nrow):for j in range(agent.env.ncol):print('%6.6s' % ('%.3f' % agent.v[i*agent.env.ncol+j]),end=' ')print()print("策略：")for i in range(agent.env.nrow):for j in range(agent.env.ncol):#一些特殊的状态，例如悬崖漫步中的悬崖if (i*agent.env.ncol+j) in disater:print('****',end=' ')elif (i*agent.env.ncol+j) in end:#目标状态print('EEEE',end=' ')else:a=agent.pi[i*agent.env.ncol+j]pi_str=''for k in range(len(action_meaning)):pi_str+=action_meaning[k] if a[k]>0 else 'o'print(pi_str,end=' ')print()#换行
env=CliffWalkingEnv()
theta=0.001
gamma=0.9
action_meaning=['↑','↓','←','→']
agent=ValueIteration(env,theta,gamma)  
agent.value_iteration()
print_agent(agent,action_meaning,list(range(37,47)),[47])
""" 解决同样的训练问题，价值迭代总共进行了数十轮，而策略迭代中策略评估总共进行了数百轮，价值迭代中的循环次数远少于策略迭代。 """