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.
By Vaneet Aggarwal
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.
By Vaneet Aggarwal
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.
By Mengxiao Zhang
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.
By David Mart\'inez-Rubio, Brian Bullins, Crist\'obal Guzm\'an, Mathieu Molina
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.
By Vaneet Aggarwal, Yiyang Lu
arXiv:2605. 21107v2 Announce Type: replace Abstract: We study constrained online convex optimization with adversarial time-varying constraints.
By Dhruv Sarkar, Abhishek Sinha
arXiv:2602. 06257v2 Announce Type: replace Abstract: Online strategic classification studies settings in which agents strategically modify their features to obtain favorable predictions.
By Chase Hutton, Adam Melrod, Han Shao
arXiv:2609. 26978v1 Announce Type: cross Abstract: We study online inverse linear optimization with a fixed unknown linear utility: in each round, an environment presents a compact action set, the learner recommends an action from it, and the environment returns an action that maximizes the utility over the same set.
By Shinsaku Sakaue
arXiv:2502. 16744v3 Announce Type: replace Abstract: In adversarial Constrained Online Convex Optimization (COCO), a learner selects actions from a fixed convex set while seeking both low regret and low cumulative constraint violation (CCV) under time-varying constraints.
By Yiyang Lu, Mohammad Pedramfar, Mengbo Wang, Vaneet Aggarwal
arXiv:2608.24731v1 Announce Type: new
Abstract: We settle the minimax-optimal alternating regret, a regret notion motivated by alternating learning dynamics in games, for both online linear optimizat...
By Yixin Tao, Weiqiang Zheng
arXiv:2608. 06825v1 Announce Type: new Abstract: Learning from correct demonstrations is harder than supervised learning when many answers are correct: after predicting, the learner sees one valid answer but not whether its own answer was valid, nor any reward.
By Pahan Dewasurendra
arXiv:2607. 19854v1 Announce Type: new Abstract: We study horizon-free regret minimization for finite-horizon time-homogeneous tabular Markov decision processes with $S$ states, $A$ actions, horizon $H$, and per-trajectory total reward bounded by $1$.
By Runlong Zhou, Zihan Zhang, Maryam Fazel, Simon S. Du