Reducing Stochastic Games to Semidefinite Program Feasibility

TL;DR

This paper introduces a polynomial-time reduction from max-plus-average constraints to semidefinite program feasibility, enabling the analysis of various stochastic and parity games through semidefinite programming techniques.

Contribution

It provides a novel polynomial-time reduction from stochastic game problems to semidefinite program feasibility, unifying different game types under a common optimization framework.

Findings

Max-plus-average constraints can be reduced to semidefinite feasibility

Stochastic mean payoff and parity games are reducible to semidefinite programming

The reduction is polynomial-time

Abstract

We present a polynomial-time reduction from max-plus-average constraints to the feasibility problem for semidefinite programs. This shows that Condon's simple stochastic games, stochastic mean payoff games, and in particular mean payoff games and parity games can all be reduced to semidefinite programming.