Comparison of Algorithms for Simple Stochastic Games

TL;DR

This paper compares three algorithm classes for simple stochastic games, introduces improvements including a quadratic programming approach, and provides the first implementation demonstrating practical speed-ups.

Contribution

It offers a comprehensive comparison of algorithms, proposes novel improvements, and presents the first implementation of quadratic programming for these games.

Findings

Improvements lead to significant speed-ups

First implementation of quadratic programming for simple stochastic games

Practical evaluation of algorithms in PRISM-games 3.0

Abstract

Simple stochastic games are turn-based 2.5-player zero-sum graph games with a reachability objective. The problem is to compute the winning probability as well as the optimal strategies of both players. In this paper, we compare the three known classes of algorithms -- value iteration, strategy iteration and quadratic programming -- both theoretically and practically. Further, we suggest several improvements for all algorithms, including the first approach based on quadratic programming that avoids transforming the stochastic game to a stopping one. Our extensive experiments show that these improvements can lead to significant speed-ups. We implemented all algorithms in PRISM-games 3.0, thereby providing the first implementation of quadratic programming for solving simple stochastic games.