Empirical Dynamic Programming

• 成果类型: Article
• 署名作者: Haskell, William B.; Jain, Rahul; Kalathil, Dileep
• 署名单位: National University of Singapore; University of Southern California; University of Southern California; University of Southern California; University of California System; University of California Berkeley
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2015.0733
• 发表日期: 2016
• 页码: 402-429
• 关键词: markov decision-processes; learning algorithms; CONVERGENCE

摘要

We propose empirical dynamic programming algorithms for Markov decision processes. In these algorithms, the exact expectation in the Bellman operator in classical value iteration is replaced by an empirical estimate to get empirical value iteration (EVI). Policy evaluation and policy improvement in classical policy iteration are also replaced by simulation to get empirical policy iteration (EPI). Thus, these empirical dynamic programming algorithms involve iteration of a random operator, the empirical Bellman operator. We introduce notions of probabilistic fixed points for such random monotone operators. We develop a stochastic dominance framework for convergence analysis of such operators. We then use this to give sample complexity bounds for both EVI and EPI. We then provide various variations and extensions to asynchronous empirical dynamic programming, the minimax empirical dynamic program, and show how this can also be used to solve the dynamic newsvendor problem. Preliminary experimental results suggest a faster rate of convergence than stochastic approximation algorithms.