On a study of Markov decision processes with unknown transition matrices

2017 Fiscal Year Final Research Report

• Project/Area Number: 26400215
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Kanagawa University
• Principal Investigator: HORIGUCHI Masayuki 神奈川大学, 理学部, 教授 (90366401)
• Co-Investigator(Kenkyū-buntansha): 中井 達 千葉大学, 教育学部, 教授 (20145808)
• Co-Investigator(Renkei-kenkyūsha): YASUDA Masami 千葉大学, 理学研究科, 名誉教授 (00041244)
• Research Collaborator: Alexey Piunovskiy ; Francois Dufour
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: マルコフ決定過程 / 推移法則未知 / ベイズ学習

Outline of Final Research Achievements

In this study, we consider the optimization problem of sequential decision processes with unknown transition probabilities. In this model with uncertainty, we formulate an optimization model with interval estimated transition probabilities from the information of observing the states of system. We derived the properties of optimal policies that are based on the representation of interval valued optimization criteria. We also consider Bayesian learning problems as the partially observed optimization problems with uncertain circumstances. In these models, we also deduced the optimization methods for optimal stopping problem and quality control problem in piecewise deterministic processes.

Free Research Field

計画数学