Using Strategy Improvement to Stay Alive

TL;DR

This paper introduces a new strategy improvement algorithm for solving Mean-Payoff Games that efficiently computes the minimum initial energy needed for a player to avoid energy depletion, outperforming existing methods in speed.

Contribution

The paper presents a novel strategy improvement algorithm for MPGs that efficiently computes minimum initial energies, providing more detailed game information and improving practical performance.

Findings

The algorithm is the fastest among existing methods for computing minimum initial energies.

It effectively utilizes strategy improvement techniques for practical efficiency.

Experimental results demonstrate superior performance over previous algorithms.

Abstract

We design a novel algorithm for solving Mean-Payoff Games (MPGs). Besides solving an MPG in the usual sense, our algorithm computes more information about the game, information that is important with respect to applications. The weights of the edges of an MPG can be thought of as a gained/consumed energy -- depending on the sign. For each vertex, our algorithm computes the minimum amount of initial energy that is sufficient for player Max to ensure that in a play starting from the vertex, the energy level never goes below zero. Our algorithm is not the first algorithm that computes the minimum sufficient initial energies, but according to our experimental study it is the fastest algorithm that computes them. The reason is that it utilizes the strategy improvement technique which is very efficient in practice.