Variance reduced value iteration and faster algorithms for solving Markov decision processes

Aaron Sidford, Mengdi Wang, Xian Wu, Yinyu Ye

Research output: Chapter in Book/Report/Conference proceedingConference contribution

8 Scopus citations

Abstract

In this paper we provide faster algorithms for approximately solving discounted Markov Decision Processes in multiple parameter regimes. Given a discounted Markov Decision Process (DMDP) with |S| states, |A| actions, discount factor γ ϵ (0; 1), and rewards in the range [-M;M], we show how to compute an ϵ-optimal policy, with probability 1 -δ in time1 Õ(( |S|2|A| + |S||A|/(1 -γ )3) log (M/ϵ) log (1/δ)) : This contribution reects the first nearly linear time, nearly linearly convergent algorithm for solving DMDP's for intermediate values of. We also show how to obtain improved sublinear time algorithms and provide an algorithm which computes an ϵ-optimal policy with probability 1-δ in time Õ (|S||A|M2/(1-γ)4ϵ2 log ( 1/δ)) provided we can sample from the transition function in O(1) time. Interestingly, we obtain our results by a careful modification of approximate value iteration. We show how to combine classic approximate value iteration analysis with new techniques in variance reduction. Our fastest algorithms leverage further insights to ensure that our algorithms make monotonic progress towards the optimal value. This paper is one of few instances in using sampling to obtain a linearly convergent linear programming algorithm and we hope that the analysis may be useful more broadly.

Original languageEnglish (US)
Title of host publication29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018
EditorsArtur Czumaj
PublisherAssociation for Computing Machinery
Pages770-787
Number of pages18
ISBN (Electronic)9781611975031
DOIs
StatePublished - Jan 1 2018
Event29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018 - New Orleans, United States
Duration: Jan 7 2018Jan 10 2018

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Other

Other29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018
CountryUnited States
CityNew Orleans
Period1/7/181/10/18

All Science Journal Classification (ASJC) codes

  • Software
  • Mathematics(all)

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  • Cite this

    Sidford, A., Wang, M., Wu, X., & Ye, Y. (2018). Variance reduced value iteration and faster algorithms for solving Markov decision processes. In A. Czumaj (Ed.), 29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018 (pp. 770-787). (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms). Association for Computing Machinery. https://doi.org/10.1137/1.9781611975031.50