Multiple Mean-Payoff Optimization under Local Stability Constraints

TL;DR

This paper introduces an efficient, scalable method for optimizing multiple mean payoffs in Markov decision processes while ensuring local stability, addressing a computationally hard problem with practical algorithms.

Contribution

It presents the first practical algorithm for simultaneous mean-payoff optimization under local stability constraints in Markov decision processes.

Findings

Developed an efficient algorithm for the problem.

Demonstrated scalability on complex models.

Achieved stable mean payoff optimization.

Abstract

The long-run average payoff per transition (mean payoff) is the main tool for specifying the performance and dependability properties of discrete systems. The problem of constructing a controller (strategy) simultaneously optimizing several mean payoffs has been deeply studied for stochastic and game-theoretic models. One common issue of the constructed controllers is the instability of the mean payoffs, measured by the deviations of the average rewards per transition computed in a finite "window" sliding along a run. Unfortunately, the problem of simultaneously optimizing the mean payoffs under local stability constraints is computationally hard, and the existing works do not provide a practically usable algorithm even for non-stochastic models such as two-player games. In this paper, we design and evaluate the first efficient and scalable solution to this problem applicable to Markov decision processes.