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.

References in corpus (8)

• SPIDER: Near-Optimal Non-Convex Optimization via Stochastic Path Integrated Differential Estimator
• Solving a Class of Non-Convex Min-Max Games Using Iterative First Order Methods
• What is Local Optimality in Nonconvex-Nonconcave Minimax Optimization?
• Mirror Descent Meets Fixed Share (and feels no regret)
• Efficient Regret Minimization in Non-Convex Games
• UniXGrad: A Universal, Adaptive Algorithm with Optimal Guarantees for Constrained Optimization
• An Online Learning Approach to Generative Adversarial Networks
• Simple Stochastic Gradient Methods for Non-Smooth Non-Convex Regularized Optimization

Cited by in corpus (2)

• Are we Forgetting about Compositional Optimisers in Bayesian Optimisation?
• Online non-convex optimization with imperfect feedback