【强化学习笔记】3.2 基于模型的策略迭代方法编程实现

重新回顾一下策略迭代算法（原理见3.1 基于模型的动态规划方法）：
（1）初始化状态值函数和状态对应的动作（初始化可以采用随机策略，即随机选择状态下的动作）
（2）遍历状态，执行状态对应的动作，得到反馈，更新状态值函数，直到状态值函数收敛
（3）遍历状态下的动作，选出收益最大的动作，作为状态对应的最终动作（贪心策略），更新状态对应的动作
（4）返回（2）直到状态对应的动作不发生变化

针对一个迷宫问题，设计基于模型的策略迭代方法。
迷宫图示见下图，其中红色部分为障碍物，绿色部分为出口：

#!/usr/bin/env python
# -*- coding:utf-8 -*-

#import gym
#import time
import random
#import numpy as np

class GriDMdp:
    def __init__(s):
        s.gamma = 0.9
        s.states = range(1,26) #状态空间
        s.actions = ['n', 'e', 's', 'w'] #动作空间
        s.terminate_states = {15:1.0, 4:-1.0, 9:-1.0, \
            11:-1.0, 12:-1.0, 23:-1.0, 24:-1.0, 25:-1.0} #½áÊø״̬
        s.trans = {} #转移矩阵
        for state in s.states:
            if not state in s.terminate_states:
                s.trans[state] = {}
        s.trans[1]['e'] = 2
        s.trans[1]['s'] = 6
        s.trans[2]['e'] = 3 
        s.trans[2]['w'] = 1
        s.trans[2]['s'] = 7
        s.trans[3]['e'] = 4
        s.trans[3]['w'] = 2
        s.trans[3]['s'] = 8
        s.trans[5]['w'] = 4
        s.trans[5]['s'] = 10
        s.trans[6]['e'] = 7
        s.trans[6]['s'] = 11
        s.trans[6]['n'] = 1
        s.trans[7]['e'] = 8
        s.trans[7]['w'] = 6 
        s.trans[7]['s'] = 12
        s.trans[7]['n'] = 2
        s.trans[8]['e'] = 9
        s.trans[8]['w'] = 7 
        s.trans[8]['s'] = 13
        s.trans[8]['n'] = 3
        s.trans[10]['w'] = 9
        s.trans[10]['s'] = 15
        s.trans[13]['e'] = 14
        s.trans[13]['w'] = 12 
        s.trans[13]['s'] = 18
        s.trans[13]['n'] = 8
        s.trans[14]['e'] = 15
        s.trans[14]['w'] = 13
        s.trans[14]['s'] = 19
        s.trans[14]['n'] = 9
        s.trans[16]['e'] = 17
        s.trans[16]['s'] = 21
        s.trans[16]['n'] = 11
        s.trans[17]['e'] = 18
        s.trans[17]['w'] = 16 
        s.trans[17]['s'] = 22
        s.trans[17]['n'] = 12
        s.trans[18]['e'] = 19
        s.trans[18]['w'] = 17 
        s.trans[18]['s'] = 23
        s.trans[18]['n'] = 13
        s.trans[19]['e'] = 20
        s.trans[19]['w'] = 18 
        s.trans[19]['s'] = 24
        s.trans[19]['n'] = 14
        s.trans[20]['w'] = 19
        s.trans[20]['s'] = 25
        s.trans[20]['n'] = 15
        s.trans[21]['e'] = 22
        s.trans[21]['n'] = 16
        s.trans[22]['e'] = 23
        s.trans[22]['w'] = 21
        s.trans[22]['n'] = 17
        
        s.rewards = {} #奖励
        for state in s.states:
            s.rewards[state] = {}
            for action in s.actions:
                s.rewards[state][action] = 0
                if state in s.trans and action in s.trans[state]:
                    next_state = s.trans[state][action]
                    if next_state in s.terminate_states:
                        s.rewards[state][action] = s.terminate_states[next_state]
        s.pi = {} #策略
        for state in s.trans:
            s.pi[state] = random.choice(s.trans[state].keys())
        s.last_pi = s.pi.copy()

        s.v = {} #状态值函数
        for state in s.states:
            s.v[state] = 0.0
    def get_random_action(s, state):
        s.pi[state] = random.choice(s.trans[state].keys())
        return s.pi[state]

    def transform(s, state, action):
        next_state = state
        state_reward = 0
        is_terminate = True
        return_info = {}

        if state in s.terminate_states:
            return next_state, state_reward, is_terminate, return_info
        if state in s.trans:    
            if action in s.trans[state]:
                next_state = s.trans[state][action]
        if state in s.rewards:
            if action in s.rewards[state]:
                state_reward = s.rewards[state][action]
        if not next_state in s.terminate_states:
            is_terminate = False
        return next_state, state_reward, is_terminate, return_info
    
    def print_states(s):
        for state in s.states:
            if state in s.terminate_states:
                print "*",
            else:
                print round(s.v[state], 2),
            if state % 5 == 0:
                print "|"
    def check_ok(s):
        last_pi_list = []
        for state in sorted(s.last_pi.keys()):
            last_pi_list.append(str(state) + "_" + s.last_pi[state])
        pi_list = []
        for state in sorted(s.pi.keys()):
            pi_list.append(str(state) + "_" + s.pi[state])
        if ",".join(last_pi_list) == ",".join(pi_list):
            return True
        else:
            s.last_pi = s.pi.copy()
            return False


        s.last_pi = s.pi.copy()

def policy_evaluate(grid_mdp):
    print "****policy_evaluate*******"
    for i in range(10000):
        delta = 0.0
        for state in grid_mdp.states:
            if state in grid_mdp.terminate_states:
                continue
            action = grid_mdp.pi[state]
            next_state, state_reward, is_terminate, return_info = grid_mdp.transform(state, action)
            q_state_action = state_reward + grid_mdp.gamma * grid_mdp.v[next_state]
            delta += abs(grid_mdp.v[state] - q_state_action)
            grid_mdp.v[state] = q_state_action
        if delta < 1e-10:
            break
    #grid_mdp.print_states()

def policy_impove(grid_mdp):
    print "****policy_impove*******"
    for state in grid_mdp.states:
        if state in grid_mdp.terminate_states:
            continue
        greedy_action = ""
        greedy_q_state_action = float('-Inf')
        for action in grid_mdp.trans[state]:
            next_state, state_reward, is_terminate, return_info = grid_mdp.transform(state, action)
            q_state_action = state_reward + grid_mdp.gamma * grid_mdp.v[next_state]
            if q_state_action > greedy_q_state_action:
                greedy_action = action
                greedy_q_state_action = q_state_action
        grid_mdp.pi[state] = greedy_action
        #print state,greedy_action

def policy_iterate(grid_mdp):
    for i in range(100):
        print i
        policy_evaluate(grid_mdp)
        policy_impove(grid_mdp)
        if grid_mdp.check_ok():
            break
grid_mdp = GriDMdp()
policy_iterate(grid_mdp)

参考书籍：

1. 深入浅出强化学习原理入门

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