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Article Dans Une Revue Open Journal of Mathematical Optimization Année : 2023

The backtrack Hölder gradient method with application to min-max and min-min problems

Jérôme Bolte
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Lilian Glaudin
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Edouard Pauwels

Résumé

We present a new algorithm to solve min-max or min-min problems out of the convex world. We use rigidity assumptions, ubiquitous in learning, making our method - the backtrack Hölder algorithm applicable to many optimization problems. Our approach takes advantage of hidden regularity properties and allows us, in particular, to devise a simple algorithm of ridge type. An original feature of our method is to come with automatic step size adaptation which departs from the usual overly cautious backtracking methods. In a general framework, we provide convergence theoretical guarantees and rates. We apply our findings on simple Generative Adversarial Network (GAN) problems obtaining promising numerical results. It is worthwhile mentioning that a byproduct of our approach is a simple recipe for general Hölderian backtracking optimization.
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Dates et versions

hal-02900875 , version 1 (16-07-2020)
hal-02900875 , version 2 (22-07-2024)

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Jérôme Bolte, Lilian Glaudin, Edouard Pauwels, Mathieu Serrurier. The backtrack Hölder gradient method with application to min-max and min-min problems. Open Journal of Mathematical Optimization, 2023, 4 (8), ⟨10.5802/ojmo.24⟩. ⟨hal-02900875v2⟩
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