Delayed Feedback in Online Non-Convex Optimization: A Non-Stationary Approach with Applications

TL;DR

This paper develops a framework for non-convex online optimization with delayed feedback, achieving sub-linear dynamic regret in non-stationary settings with applications to bandit problems and practical quadratic fractional functions.

Contribution

It introduces a non-stationary approach for non-convex delayed-noise online optimization, establishing bounded dynamic regret for quasar-convex functions under various smoothness conditions.

Findings

Achieves sub-linear dynamic regret in non-stationary settings.

Extends quasar-convexity to new classes of functions, including strongly quasiconvex functions.

Validates theoretical results with numerical experiments.

Abstract

We study non-convex delayed-noise online optimization problems by evaluating dynamic regret in the non-stationary setting when the loss functions are quasar-convex. In particular, we consider scenarios involving quasar-convex functions either with a Lipschitz gradient or weakly smooth and, for each case, we ensure bounded dynamic regret in terms of cumulative path variation achieving sub-linear regret rates. Furthermore, we illustrate the flexibility of our framework by applying it to both theoretical settings such as zeroth-order (bandit) and also to practical applications with quadratic fractional functions. Moreover, we provide new examples of non-convex functions that are quasar-convex by proving that the class of differentiable strongly quasiconvex functions (Polyak 1966) are strongly quasar-convex on convex compact sets. Finally, several numerical experiments validate our theoretical findings, illustrating the effectiveness of our approach.