TY - JOUR

T1 - Life is Random, Time is Not: Markov Decision Processes with Window Objectives

AU - Brihaye, Thomas

AU - Delgrange, Florent

AU - Oualhadj, Youssouf

AU - Randour, Mickael

PY - 2020/12/14

Y1 - 2020/12/14

N2 - The window mechanism was introduced by Chatterjee et al. to strengthen classical game objectives with time bounds. It permits to synthesize system controllers that exhibit acceptable behaviors within a configurable time frame, all along their infinite execution, in contrast to the traditional objectives that only require correctness of behaviors in the limit. The window concept has proved its interest in a variety of two-player zero-sum games because it enables reasoning about such time bounds in system specifications, but also thanks to the increased tractability that it usually yields. In this work, we extend the window framework to stochastic environments by considering Markov decision processes. A fundamental problem in this context is the threshold probability problem: given an objective it aims to synthesize strategies that guarantee satisfying runs with a given probability. We solve it for the usual variants of window objectives, where either the time frame is set as a parameter, or we ask if such a time frame exists. We develop a generic approach for window-based objectives and instantiate it for the classical mean-payoff and parity objectives, already considered in games. Our work paves the way to a wide use of the window mechanism in stochastic models.

AB - The window mechanism was introduced by Chatterjee et al. to strengthen classical game objectives with time bounds. It permits to synthesize system controllers that exhibit acceptable behaviors within a configurable time frame, all along their infinite execution, in contrast to the traditional objectives that only require correctness of behaviors in the limit. The window concept has proved its interest in a variety of two-player zero-sum games because it enables reasoning about such time bounds in system specifications, but also thanks to the increased tractability that it usually yields. In this work, we extend the window framework to stochastic environments by considering Markov decision processes. A fundamental problem in this context is the threshold probability problem: given an objective it aims to synthesize strategies that guarantee satisfying runs with a given probability. We solve it for the usual variants of window objectives, where either the time frame is set as a parameter, or we ask if such a time frame exists. We develop a generic approach for window-based objectives and instantiate it for the classical mean-payoff and parity objectives, already considered in games. Our work paves the way to a wide use of the window mechanism in stochastic models.

KW - Computer Science

KW - Logic in Computer Science

KW - Artificial Intelligence

KW - Formal Languages and Automata Theory

KW - Game Theory

KW - Mathematics - Probability

UR - http://www.scopus.com/inward/record.url?scp=85101636509&partnerID=8YFLogxK

U2 - 10.23638/LMCS-16(4:13)2020

DO - 10.23638/LMCS-16(4:13)2020

M3 - Article

VL - 16

SP - 13:1-13:30

JO - Logical Methods in Computer Science

JF - Logical Methods in Computer Science

SN - 1860-5974

IS - 4

ER -