# Frequency-Based Hyperparameter Selection in Games

arXiv: https://arxiv.org/abs/2601.18409 · HTML: https://mlsanity.com/paper/2601.18409/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 35 references that are in the map.
- First posted on arXiv 26 Jan 2026.

## Builds on (most cited first, 10 of 10)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Lookahead Optimizer: k steps forward, 1 step back](https://mlsanity.com/paper/1907.08610/) (2019)
- [The Mechanics of n-Player Differentiable Games](https://mlsanity.com/paper/1802.05642/) (2018)
- [Halpern Iteration for Near-Optimal and Parameter-Free Monotone Inclusion and Strong Solutions to Variational Inequalities](https://mlsanity.com/paper/2002.08872/) (2020)
- [ODE Analysis of Stochastic Gradient Methods with Optimism and Anchoring for Minimax Problems](https://mlsanity.com/paper/1905.10899/) (2019)
- [Taming GANs with Lookahead-Minmax](https://mlsanity.com/paper/2006.14567/) (2020)
- [Last-Iterate Convergence of Saddle-Point Optimizers via High-Resolution Differential Equations](https://mlsanity.com/paper/2112.13826/) (2021)
- [Frequency-Domain Representation of First-Order Methods: A Simple and Robust Framework of Analysis](https://mlsanity.com/paper/2109.04603/) (2021)

## Abstract (arXiv)

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 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.