2022/05/25 by Elias Wirth, Wirth, Elias, Thomas Kerdreux +3 · 3 citations
Computer Science · Decision Sciences · #Advanced Bandit Algorithms Research #FOS: Mathematics #Machine Learning and Algorithms #Optimization and Control (math.OC) #Stochastic Gradient Optimization Techniques
paper · pdf · doi:10.48550/arxiv.2205.12838
openalex publication_date 2022/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Frank-Wolfe algorithms (FW) are popular first-order methods for solving constrained convex optimization problems that rely on a linear minimization oracle instead of potentially expensive projection-like oracles. Many works have identified accelerated convergence rates under various structural assumptions on the optimization problem and for specific FW variants when using line-search or short-step, requiring feedback from the objective function. Little is known about accelerated convergence regimes when utilizing open-loop step-size rules, a.k.a. FW with pre-determined step-sizes, which are algorithmically extremely simple and stable. Not only is FW with open-loop step-size rules not always subject to the same convergence rate lower bounds as FW with line-search or short-step, but in some specific cases, such as kernel herding in infinite dimensions, it has been empirically observed that FW with open-loop step-size rules enjoys to faster convergence rates than FW with line-search or short-step. We propose a partial answer to this unexplained phenomenon in kernel herding, characterize a general setting for which FW with open-loop step-size rules converges non-asymptotically faster than with line-search or short-step, and derive several accelerated convergence results for FW with open-loop step-size rules. Finally, we demonstrate that FW with open-loop step-sizes can compete with momentum-based open-loop FW variants.