Non-oblivious Strategy Improvement

TL;DR

This paper introduces non-oblivious strategy improvement algorithms for mean-payoff and parity games that leverage structural properties of the game to enhance performance, especially on challenging instances.

Contribution

It presents a novel class of algorithms that remember game structures, improving upon oblivious methods by accelerating convergence on difficult cases.

Findings

Non-oblivious algorithms outperform oblivious ones on hard examples.

Structural awareness leads to faster strategy improvement.

Previous algorithms fail due to ignoring game structures.

Abstract

We study strategy improvement algorithms for mean-payoff and parity games. We describe a structural property of these games, and we show that these structures can affect the behaviour of strategy improvement. We show how awareness of these structures can be used to accelerate strategy improvement algorithms. We call our algorithms non-oblivious because they remember properties of the game that they have discovered in previous iterations. We show that non-oblivious strategy improvement algorithms perform well on examples that are known to be hard for oblivious strategy improvement. Hence, we argue that previous strategy improvement algorithms fail because they ignore the structural properties of the game that they are solving.