Symmetric Strategy Improvement

TL;DR

This paper introduces a symmetric strategy improvement algorithm for two-player zero-sum games that improves both players' strategies simultaneously, overcoming previous limitations and challenges in the field.

Contribution

It presents a novel symmetric strategy improvement method that avoids Friedmann's traps, advancing the analysis and solution techniques for parity, mean-payoff, and discounted-payoff games.

Findings

Symmetric strategy improvement defies Friedmann's traps.

The algorithm improves strategies of both players simultaneously.

It challenges the belief that classic strategy improvement can be polynomial.

Abstract

Symmetry is inherent in the definition of most of the two-player zero-sum games, including parity, mean-payoff, and discounted-payoff games. It is therefore quite surprising that no symmetric analysis techniques for these games exist. We develop a novel symmetric strategy improvement algorithm where, in each iteration, the strategies of both players are improved simultaneously. We show that symmetric strategy improvement defies Friedmann's traps, which shook the belief in the potential of classic strategy improvement to be polynomial.