arXiv:2610. 00545v1 Announce Type: new Abstract: We study adversarial online maximization of nonnegative, non-monotone DR-submodular functions over compact convex down-closed sets.
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arXiv:2609.38375v1 Announce Type: new Abstract: Can a constant number of linear minimizations per round improve on the $T^{3/4}$ regret rate of online Frank-Wolfe on general convex sets? Weibel et al...
arXiv:2608. 25182v1 Announce Type: cross Abstract: In this paper, we study alternating regret in online convex optimization (OCO), motivated by the success of alternating learning dynamics in two-player games.
The paper presents an online algorithm that achieves the same $0.401$ approximation factor for maximizing nonnegative, non-monotone DR-submodular functions over compact convex down-closed subsets of the $d$-dimensional unit cube as the best known offline construction. In the full-information value-oracle model, the algorithm attains this factor with sublinear regret, using $O(dT^{1/4})$ oracle calls per round and $O(T^{3/4})$ regret, and offers flexible batching trade-offs. Under a positive-anchor condition, a randomized blocking strategy preserves the $0.401$ factor while achieving $O(T^{5/6})$ one-point bandit regret.
arXiv:2609. 20687v1 Announce Type: cross Abstract: We study first-order black-box convex optimization over an $\ell_p$-ball for objectives Lipschitz in the $\ell_q$-norm, solving in the affirmative the nonsmooth version of the COLT open question (Guz15b) on whether the geometry of a smaller feasible set ($p < q$) can improve convergence rates in convex optimization, and matching prior lower bounds up to logarithmic factors.
The paper studies online convex optimization when the learner can only query an exact linear optimization oracle. It establishes a dimension‑free minimax expected regret bound of θ(GD max{√T, T/(1+min{Q,BT})^{1/4}}) for convex G‑Lipschitz losses, where Q is the total oracle budget and B the per‑round limit. The authors provide matching lower and upper bounds, showing how strict per‑round or total‑budget constraints affect the achievable regret, and extend the analysis to smooth losses with curvature‑dependent bounds.
arXiv:2605. 09454v2 Announce Type: replace-cross Abstract: We study the $\textit{single-index bandit}$ problem, where rewards depend on an unknown one-dimensional projection of high-dimensional contexts through an unknown reward function.