Regret minimization in stochastic non-convex learning via a proximal-gradient approach

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 me...

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Bibliographic Details
Published in:arXiv.org 2020-10
Main Authors: Hallak, Nadav, Mertikopoulos, Panayotis, Cevher, Volkan
Format: Article
Language:English
Subjects:
Feedback
Machine learning
Mapping
Operations research
Optimization
Online Access:Get full text
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Summary: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.
ISSN:2331-8422