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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.17053 |
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Table of Contents:
- 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.