2020/07/17 by Jérôme Bolte, Lilian Glaudin, Bolte, Jérôme +6 · 4 citations
Computer Science · Engineering · Mathematics · #Algorithm #Backtracking #Computer science #Convergence (economics) #FOS: Computer and information sciences #FOS: Mathematics #Feature (linguistics) #Machine Learning (cs.LG) #Machine Learning and Algorithms #Mathematical optimization #Mathematics #Optimization and Control (math.OC) #Regular polygon #Rigidity (electromagnetism) #Simple (philosophy) #Sparse and Compressive Sensing Techniques #Stochastic Gradient Optimization Techniques #cs.LG #math.OC
paper · pdf · doi:10.48550/arxiv.2007.08810
published in arXiv (Cornell University) (Cornell University)
arxiv created 2020/07/17 · openalex publication_date 2020/07/17 · arxiv updated 2020/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.