arXiv:2607. 27073v1 Announce Type: new Abstract: We study online convex optimization (OCO) in non-stationary environments under heavy-tailed noise, where the stochastic gradient oracle admits only a finite $p$-th central moment for some $p \in (1, 2]$.
arXiv:2607. 27073v2 Announce Type: replace-cross Abstract: We study online convex optimization with stochastic gradient noise whose conditional $p$-th central moment is bounded by $\sigma^p$, for an unknown $p\in(1,2]$.
arXiv:2609. 06921v1 Announce Type: cross Abstract: We study constrained online convex optimization with adversarial constraints when constraint values and gradients are observed through unbiased noise.
The paper studies contextual bilateral trade with full feedback, showing that action-independent observations eliminate the usual polynomial adaptation penalty seen in heavy-tailed bandits. It presents fully parameter-free algorithms that achieve oracle minimax regret rates without knowing the moment order or scale, and derives new regret bounds for both parametric and nonparametric settings. The key technical insight is a paired squared‑loss statistic whose noise cancels, enabling model selection and yielding regret rates that interpolate between classical nonparametric and linear extremes.
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:2607. 17607v1 Announce Type: new Abstract: We study whether stochastic nonconvex optimization can be reduced to ordinary static regret minimization in online convex optimization in a black-box manner.
arXiv:2609. 30556v1 Announce Type: new Abstract: We study dynamic regret in online convex optimization with an \emph{indicator switching cost}: a fixed penalty incurred whenever two consecutive decisions differ.
arXiv:2606. 08028v1 Announce Type: new Abstract: We study high-probability regret bounds for online convex optimization (OCO) with strongly convex losses and establish three results that resolve open questions at the intersection of noise adaptivity, feedback structure, and constraint satisfaction.
arXiv:2602. 06902v3 Announce Type: replace Abstract: In this paper, we study dynamic regret in unconstrained online convex optimization (OCO) with movement costs.
arXiv:2603. 25029v4 Announce Type: replace Abstract: We study online convex optimization (OCO) with two-point bandit feedback against a non-anticipating adaptive adversary.
The paper introduces a straightforward framework that transforms dynamic regret minimization into switching regret minimization by constructing an unbiased random sequence for any comparator sequence. Using this reduction, the authors derive dynamic regret bounds for strongly convex and exp-concave losses of “~O(T^{1/3}P_T^{2/3})” and for general convex losses of “O(√{T(1+P_T)})”, matching known minimax optimal results. The approach leverages off-the-shelf switching regret algorithms and controlled variance to achieve these bounds.
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.
arXiv:2605. 21107v2 Announce Type: replace Abstract: We study constrained online convex optimization with adversarial time-varying constraints.