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.
Related stories
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
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 \(S_1 \supseteq S_2 \supseteq \cdots \supseteq S_T\).
arXiv Machine Learning
Jun 3
From Non-Convex to Strongly Convex: Curvature-Adaptive FTPL for Online Optimization
arXiv:2606. 02948v1 Announce Type: new Abstract: Curvature adaptivity is a classical theme in online optimization: for convex Lipschitz losses, adaptive methods interpolate between the optimal $O(\sqrt{T})$ regret for general convex losses and $O(\log T)$ regret under strong convexity.
arXiv Machine Learning
2d ago
Curvature-Independent Regret Bounds for Distributed Online Optimization on Hadamard Manifolds
arXiv:2609. 13646v1 Announce Type: new Abstract: This work addresses decentralized online Riemannian optimization on Hadamard manifolds.
arXiv Machine Learning
6d ago
Convex Optimization with Nested Evolving Feasible Sets (CONES) under Time-Varying Loss Functions
arXiv:2609. 11207v1 Announce Type: new Abstract: Convex Optimization with Nested Evolving Feasible Sets (CONES)} was introduced in \cite{CONESVaze} where the objective function \(f\) remains fixed but the feasible region evolves over time as a nested sequence \(S_1 \supseteq S_2 \supseteq \cdots \supseteq S_T\).
arXiv Machine Learning
Jun 25
A Geometry-Aware Efficient Algorithm for Compositional Entropic Risk Minimization
arXiv:2602. 02877v2 Announce Type: replace Abstract: This paper studies optimization for a family of problems termed $\textbf{compositional entropic risk minimization}$, in which each data's loss is formulated as a Log-Expectation-Exponential (Log-E-Exp) function.
arXiv Machine Learning
Jul 14
Bandit PCA with Minimax Optimal Regret
arXiv:2607. 10936v1 Announce Type: new Abstract: We study the bandit-feedback version of online principal component analysis (Bandit PCA): in each round $t = 1,\dots,T$, the adversary selects a $d \times d$ symmetric gain matrix $G_t$ with spectrum in $[0,1]$ and rank at most $r$; the learner simultaneously selects a unit vector $w_t \in S^{d-1}$ and receives the reward $w_t^\top G_t w_t$.