Analysis of Kernel Mirror Prox for Measure Optimization

arXiv:2403.00147v1 Announce Type: cross
Abstract: By choosing a suitable function space as the dual to the non-negative measure cone, we study in a unified framework a class of functional saddle-point optimization problems, which we term the Mixed Functional Nash Equilibrium (MFNE), that underlies several existing machine learning algorithms, such as implicit generative models, distributionally robust optimization (DRO), and Wasserstein barycenters. We model the saddle-point optimization dynamics as an interacting Fisher-Rao-RKHS gradient flow when the function space is chosen as a …

abstract algorithms analysis arxiv class cs.lg equilibrium framework function functional generative kernel machine machine learning machine learning algorithms math.oc mixed nash equilibrium negative optimization space study type