A Hölderian backtracking method for min-max and min-min problems

Jérôme Bolte, Lilian Glaudin, Edouard Pauwels and Matthieu Serrurier

No 21-1243, TSE Working Papers from Toulouse School of Economics (TSE)

Abstract: 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 applicable to many optimization problems. Our approach takes advantage of hidden regularity properties and allows us 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 GAN problems obtaining promising numerical results

Date: 2021-09
New Economics Papers: this item is included in nep-isf
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