Regret minimization in stochastic non-convex learning via a proximal-gradient approach
Abstract
Motivated by applications in machine learning and operations research, we study regret minimization with stochastic first-order oracle feedback in online constrained, and possibly non-smooth, non-convex problems. In this setting, the minimization of external regret is beyond reach for first-order methods, so we focus on a local regret measure defined via a proximal-gradient mapping. To achieve no (local) regret in this setting, we develop a prox-grad method based on stochastic first-order feedback, and a simpler method for when access to a perfect first-order oracle is possible. Both methods are min-max order-optimal, and we also establish a bound on the number of prox-grad queries these methods require. As an important application of our results, we also obtain a link between online and offline non-convex stochastic optimization manifested as a new prox-grad scheme with complexity guarantees matching those obtained via variance reduction techniques.
Cite
@article{arxiv.2010.06250,
title = {Regret minimization in stochastic non-convex learning via a proximal-gradient approach},
author = {Nadav Hallak and Panayotis Mertikopoulos and Volkan Cevher},
journal= {arXiv preprint arXiv:2010.06250},
year = {2020}
}