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
Jérôme Bolte, Lilian Glaudin, Edouard Pauwels et Matthieu Serrurier, « A Hölderian backtracking method for min-max and min-min problems », TSE Working Paper, n° 21-1243, septembre 2021.
TSE Working Paper, n° 21-1243, septembre 2021