马尔科夫决策过程MDP - Lecture Note for CS188(暨CS181 ShanghaiTech)

版权声明：博客为个人原创，如需转载请注明出处 https://blog.csdn.net/liubai01/article/details/84441464

说明：笔记旨在整理我校CS181课程的基本概念(PPT借用了Berkeley CS188)。由于授课及考试语言为英文，故英文出没可能。

目录

 

1 Markov Decision Processes mechanics

1.1 Markov Decision definitions

1.2 Markov 涵义

1.3 最优策略optimal policy

1.4  MDP搜索树 MDP search tree

2 Solving MDPs

2.1 Optimal Quantities

2.2 Value of states

2.3 Value iteration

2.4 Policy iteration

Reference

---

1 Markov Decision Processes mechanics

1.1 Markov Decision definitions

A MDP is defined by: 

1.2 Markov 涵义

For markov decision processes, "Markov" means action outcomes depend only on the current state:

1.3 最优策略optimal policy

For MDP, we want an optimal policy :

• A policy π gives an action for each state
• An optimal policy is one that maximizes expected utility if allowed
• An explicity policy defines a reflex agent

1.4  MDP搜索树 MDP search tree

5. Discounting: each time we descend a level, we multiply in the discount once. Redefine Rewards R(s, a, s') with discount γ

2 Solving MDPs

2.1 Optimal Quantities

1. The value (utility) of a state s: =expected utility starting in s and acting optimally.

2. The value (utility) of a q-state (s,a): =expected utility starting out having taken action a from state s and (therefore) acting optimally

3. The optimal policy: =optimal action from state s

2.2 Value of states

2.3 Value iteration

1.Define  to be the optimal value of s if the game ends in k more time steps

time-limited value evaluation

2.Policy extraction

2.4 Policy iteration

Step1 Policy evaluation:

Step2: Policy improvement: After evaluation(step 1), we get 

Policy iteration: repeat two steps until policy converges

Reference

1. Artificial Intelligence, A Modern Approach. 3rd Edition. Stuart R., Peter N. Chapter 17

2. UC berkeley, CS188. Lecture 13 Markov Decision Process