2022/11/22 by Lu Zhou, Lu, Zhou, Nataly Brukhim +5 · 1 citation
Computer Science · Decision Sciences · Engineering · #Advanced Bandit Algorithms Research #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques #Stochastic Gradient Optimization Techniques
paper · pdf · doi:10.48550/arxiv.2211.12638
openalex publication_date 2022/11/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 HK12 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 GK22 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 Mhammedi22, 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 O(√(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.