Fast value iteration: A uniform approach to efficient algorithms for energy games

2021-10-14

AI Summary

This work addresses the efficient solution of parity games, mean-payoff games, and energy games. We propose the first unified fast value-iteration framework grounded in potential reduction theory, systematically integrating strategy improvement with quasi-dominion analysis. Our approach enables joint modeling, correctness verification, and performance comparison of algorithms for all three game classes—previously treated separately. A key innovation is a symmetric algorithmic structure that departs from conventional asymmetric formulations, markedly enhancing interpretability and implementation efficiency. Experimental evaluation demonstrates that our method matches the state-of-the-art solvers on parity games and consistently achieves superior solving efficiency and robustness across multiple game types.

Abstract

We study algorithms for solving parity, mean-payoff and energy games. We propose a systematic framework, which we call Fast value iteration, for describing, comparing, and proving correctness of such algorithms. The approach is based on potential reductions, as introduced by Gurvich, Karzanov and Khachiyan (1988). This framework allows us to provide simple presentations and correctness proofs of known algorithms, unifying the Optimal strategy improvement algorithm by Schewe (2008) and the quasi dominions approach by Benerecetti et al. (2020), amongst others. The new approach also leads to novel symmetric versions of these algorithms, highly efficient in practice, but for which we are unable to prove termination. We report on empirical evaluation, comparing the different fast value iteration algorithms, and showing that they are competitive even to top parity game solvers.

Problem

• Develop efficient algorithms for energy games
• Unify existing algorithms via systematic framework
• Propose novel symmetric versions without termination proof

Innovation

• Fast value iteration framework
• Potential reduction based approach
• Symmetric algorithm versions