Frequency-Based Hyperparameter Selection in Games

TL;DR

This paper introduces Modal LookAhead (MoLA), a frequency-based hyperparameter tuning method for games that adaptively selects parameters to accelerate training and improve convergence, addressing challenges posed by rotational dynamics.

Contribution

The paper proposes MoLA, a novel frequency-based hyperparameter selection method for games, with theoretical guarantees and practical improvements over existing approaches.

Findings

MoLA accelerates training in rotational and mixed games.

MoLA provides convergence guarantees.

MoLA has minimal computational overhead.

Abstract

Learning in smooth games fundamentally differs from standard minimization due to rotational dynamics, which invalidate classical hyperparameter tuning strategies. Despite their practical importance, effective methods for tuning in games remain underexplored. A notable example is LookAhead (LA), which achieves strong empirical performance but introduces additional parameters that critically influence performance. We propose a principled approach to hyperparameter selection in games by leveraging frequency estimation of oscillatory dynamics. Specifically, we analyze oscillations both in continuous-time trajectories and through the spectrum of the discrete dynamics in the associated frequency-based space. Building on this analysis, we introduce \emph{Modal LookAhead (MoLA)}, an extension of LA that selects the hyperparameters adaptively to a given problem. We provide convergence guarantees and demonstrate in experiments that MoLA accelerates training in both purely rotational games and mixed regimes, all with minimal computational overhead.