arXiv Machine Learning
Jul 15
A Geometric Approach to Constrained Online Learning
arXiv:2605. 21107v2 Announce Type: replace Abstract: We study constrained online convex optimization with adversarial time-varying constraints.
Block-Norm Geometries for Online Mirror Descent with Sparse Losses
The paper investigates how the choice of geometry in online mirror descent affects performance, particularly when loss gradients are sparse. It introduces randomized block‑norm mirror maps that interpolate between Euclidean and entropic geometries, achieving polynomial‑in‑dimension regret improvements over standard methods for various convex sets. The authors also demonstrate that naive alternation between mirror maps can lead to linear regret and propose a Hedge‑based meta‑algorithm that competes with the best mirror map in a finite portfolio, achieving near‑optimal regret for random block geometries.
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arXiv Machine Learning
Sep 18
The First-Order Oracle Complexity of Lipschitz Convex Optimization in Nondual Settings
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.
arXiv Machine Learning
Sep 23
Exact-Form Regret for Gradient Descent, Mirror Descent and Follow-the-Regularized-Leader
arXiv:2609.09466v2 Announce Type: replace Abstract: Online gradient descent is usually studied through external regret, where the learner competes with fixed alternatives. Recent work shows that firs...
arXiv Machine Learning
Oct 3
Sharp Oracle-Regret Tradeoffs for Projection-Free Online Convex Optimization
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 Machine Learning
Jun 17
Provably Efficient Regularized Online RLHF with Generalized Bilinear Preferences
arXiv:2602. 23116v3 Announce Type: replace Abstract: We consider the problem of regularized best-response max-regret minimization in online RLHF under general preferences and bandit feedback.
arXiv Machine Learning
Oct 15
Tracking a Small Set of Experts in Online Convex Optimization
arXiv:2610.20416v1 Announce Type: new Abstract: For the fundamental problem of prediction from expert advice, Freund asked whether one could compete with a comparator that switches $k$ times among on...
arXiv Machine Learning
Sep 24
Tight Regret Bound for Online Inverse Linear Optimization via Multiscale Matrix Weights
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.
arXiv Machine Learning
Jun 2
Mirror Descent Under Generalized Smoothness
arXiv:2502. 00753v4 Announce Type: replace-cross Abstract: Smoothness is crucial for attaining fast rates in first-order optimization.
arXiv AI
Sep 1
Nested Convex-Body Chasing for Online Optimization with Evolving Feasible Sets
arXiv:2608.29074v1 Announce Type: new Abstract: We study online optimization with nested shrinking feasible regions in two settings: convex optimization with nested evolving feasible sets (CONES) and...
arXiv Machine Learning
Aug 18
Online Convex Optimization with Dueling Feedback
arXiv:2608. 15050v1 Announce Type: new Abstract: We study online convex optimization with dueling (pairwise comparison) feedback, where the learner observes only a binary preference between two queried points.
arXiv Machine Learning
Jun 19
The Hidden Cost of Approximation in Online Mirror Descent
arXiv:2511. 22283v2 Announce Type: replace Abstract: Online mirror descent (OMD) is a fundamental algorithmic paradigm that underlies many algorithms in optimization, machine learning and sequential decision-making.
arXiv Machine Learning
Aug 18
Convex Optimization with Nested Evolving Feasible Sets
arXiv:2605. 07386v2 Announce Type: replace Abstract: \emph{Convex Optimization with Nested Evolving Feasible Sets (CONES)} is considered where the objective function \(f\) remains fixed but the feasible region evolves over time as a nested sequence \(S_1 \supseteq S_2 \supseteq \cdots \supseteq S_T\).