Tracking and Regret Bounds for Online Zeroth-Order Euclidean and Riemannian Optimization

Online Submodular Maximization via Online Convex Optimization

“…In the full information setting, the OSM algorithm by Harvey, Liaw, and Soma (2020) has a slightly tighter α-regret than us, but also a much higher computational complexity. We attain the same or better regret than DR-S (Chen, Hassani, and Karbasi 2018;Zhang et al 2019Zhang et al , 2022 and remaining algorithms that either operate on restricted constraint sets (Niazadeh et al 2021;Matsuoka, Ito, and Ohsaka 2021;Streeter, Golovin, and Krause 2009) or on the much more restrictive LWD class (Kakade, Kalai, and Ligett 2007). Most importantly, our work generalizes to the dynamic and optimistic settings.…”

“…OSM via Regret Minimization. Several online algorithms have been proposed for maximizing general submodular functions (Niazadeh et al 2021;Harvey, Liaw, and Soma 2020;Matsuoka, Ito, and Ohsaka 2021;Streeter, Golovin, and Krause 2009) under different matroid constraints. There has also been recent work (Chen, Hassani, and Karbasi 2018;Zhang et al 2019Zhang et al , 2022 on the online maximization of continuous DR-submodular functions (Bach 2019).…”

“…Most importantly, our work generalizes to the dynamic and optimistic settings. With the exception of Matsuoka, Ito, and Ohsaka (2021), who study dynamic regret restricted to uniform matroids, our work provides the first guarantees for OSM in the dynamic and optimistic settings under general matroid constraints. OSM in the Bandit Setting.…”

“…The objective is to minimize α-regret, i.e., the difference of the cumulative reward accrued from the one attained by a static set, selected by an α-approximation algorithm operating in hindsight. OSM has received considerable interest recently, both in the full information (Harvey, Liaw, and Soma 2020;Matsuoka, Ito, and Ohsaka 2021;Streeter, Golovin, and Krause 2009;Niazadeh et al 2021) and bandit setting (Niazadeh et al 2021;Matsuoka, Ito, and Ohsaka 2021;Wan et al 2023), where only the reward values (rather than the entire functions) are revealed.…”

A Survey on Distributed Online Optimization and Game

“…Aside from the Euclidean space studied for DOL in the literature, Remannian manifolds, as a generalization of Euclidean spaces, have long been an intriguing topic in deep learning and centralized/decentralized optimization, possessing a large number of applications such as in principal component analysis (PCA), independent component analysis (ICA), radar signal processing, dictionary learning, and mixture modeling [144]. However, the study of DOL on Remannian manifolds is still missing, only having a few works on the centralized setup [145], [146], thereby posing the necessity of addressing this case in future. 10) The Case with Switching Cost.…”