Projection-free Adaptive Regret with Membership Oracles

Zhou Lu, Nataly Brukhim, Paula Gradu, Elad Hazan

Research output: Contribution to journalConference articlepeer-review

1 Scopus citations

Abstract

In the framework of online convex optimization, most iterative algorithms require the computation of projections onto convex sets, which can be computationally expensive. To tackle this problem Hazan and Kale (2012) proposed the study of projection-free methods that replace projections with less expensive computations. The most common approach is based on the Frank-Wolfe method, that uses linear optimization computation in lieu of projections. Recent work by Garber and Kretzu (2022) gave sublinear adaptive regret guarantees with projection free algorithms based on the Frank Wolfe approach. In this work we give projection-free algorithms that are based on a different technique, inspired by Mhammedi (2022), that replaces projections by set-membership computations. We propose a simple lazy gradient-based algorithm with a Minkowski regularization that attains near-optimal adaptive regret bounds. For general convex loss functions we improve previous adaptive regret bounds from O(T3/4) to O(T), and further to tight interval dependent bound Õ(I) where I denotes the interval length. For strongly convex functions we obtain the first poly-logarithmic adaptive regret bounds using a projection-free algorithm.

Original languageEnglish (US)
Pages (from-to)1055-1073
Number of pages19
JournalProceedings of Machine Learning Research
Volume201
StatePublished - 2023
Event34th International Conference onAlgorithmic Learning Theory, ALT 2023 - Singapore, Singapore
Duration: Feb 20 2023Feb 23 2023

All Science Journal Classification (ASJC) codes

  • Artificial Intelligence
  • Software
  • Control and Systems Engineering
  • Statistics and Probability

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