Strengthening the finite characterizations of smooth min-max games
Abstract
In this paper, we address the problem of interpolation of smooth convex-concave functions. Interpolation is a key step for computer-assisted estimation of worst-case performance via PEP-like techniques, and smooth convex-concave functions are frequently used to model min-max problems arising in machine learning. We address the challenges associated with deriving conditions that are necessary and sufficient for the interpolation of smooth min-max games and show how existing approaches can be adapted to this setting. As part of this effort, we study the smoothing properties of Moreau-Yosida-like approximations of convex-concave functions. Next, we derive interpolation conditions for several key special cases of smooth min-max games. Finally, we obtain improved (i.e., tighter) characterizations for smooth strongly monotone convex-concave functions. We analyze the linear convergence of Alt-GDA using a PEP-like technique with novel constraints and (numerically) obtain a new estimate of its complexity. We are confident that the results of this paper provide meaningful progress toward establishing optimal worst-case guarantees for algorithms in the setting of smooth min-max games.
Keywords
Cite
@article{arxiv.2603.17053,
title = {Strengthening the finite characterizations of smooth min-max games},
author = {Valery Krivchenko and Alexander Gasnikov and Dmitry Kovalev},
journal= {arXiv preprint arXiv:2603.17053},
year = {2026}
}
Comments
We found serious errors that invalidate the main results and conclusions of the paper. The first errors appear in Lemma 7 (Subsection 3.5) which is simply wrong, and Lemma 8. Consequently, the results of Lemmas 9, 10, 11, 12 and Theorems 4,7,8,9 are invalid. Theorems 8 and 9 are the core results of this paper. We are certain that the situation justifies withdrawal