Data-Driven Performance Guarantees for Classical and Learned Optimizers

arXiv:2404.13831v1 Announce Type: cross
Abstract: We introduce a data-driven approach to analyze the performance of continuous optimization algorithms using generalization guarantees from statistical learning theory. We study classical and learned optimizers to solve families of parametric optimization problems. We build generalization guarantees for classical optimizers, using a sample convergence bound, and for learned optimizers, using the Probably Approximately Correct (PAC)-Bayes framework. To train learned optimizers, we use a gradient-based algorithm to directly minimize the PAC-Bayes upper bound. Numerical experiments in …

abstract algorithms analyze arxiv build continuous convergence cs.lg data data-driven families math.oc optimization parametric performance sample solve statistical study theory type