arXiv:2608. 22834v2 Announce Type: replace-cross Abstract: We derive convergence guarantees for mirror descent and proximal mirror descent with a logarithmic barrier as the distance-generating function.
arXiv:2608. 07248v1 Announce Type: cross Abstract: We prove that mirror descent converges to a KKT point for the nonconvex problem without excluding boundary limits.
arXiv:2502. 00753v4 Announce Type: replace-cross Abstract: Smoothness is crucial for attaining fast rates in first-order optimization.
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.
The paper studies algorithms for computing the Entropic Gromov-Wasserstein (EGW) distance, a measure of discrepancy between metric measure spaces. It introduces Averaged Mirror Descent (AMD), which averages successive Mirror Descent steps and is proven to converge for any cost function, and shows that a dual gradient method with a fixed step size also converges for arbitrary costs, even when iterations are inexact. Empirical comparisons demonstrate that both AMD and the dual gradient method succeed on cases where classical Mirror Descent fails.
arXiv:2504.09409v3 Announce Type: replace-cross Abstract: In this paper, we study nonconvex constrained stochastic zeroth-order optimization problems with exact constraints and stochastic objective e...
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.
arXiv:2606.23198v2 Announce Type: replace-cross Abstract: We study mirror flows generated by a convex quadratic loss and a general convex lower semicontinuous mirror potential. We show that, when ini...
arXiv:2610.15829v2 Announce Type: replace Abstract: Hard-margin SVM training is the distance problem between two convex hulls, which the Triangle Algorithm (TA) solves with a certified duality gap. W...
arXiv:2606. 03769v1 Announce Type: cross Abstract: We study the robustness of stochastic mirror descent (SMD) under heavy-tailed noise, focusing on whether the method retains its convergence guarantees when run with infinite-variance stochastic gradient input.
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:2608. 08463v1 Announce Type: cross Abstract: We study second- and higher-order methods for solving smooth monotone variational inequalities (MVI).
The paper introduces a conversion scheme that transforms regret-minimizing algorithms into fixed-point iterations, providing convergence guarantees derived from regret bounds. This framework generalizes the classical Krasnoselskii–Mann iterations, recovering them when applying Online Gradient Descent. By converting AdaGrad-based regret minimizers, the authors obtain new fixed-point iterations with adaptive guarantees, and numerical experiments show these AdaGrad-based iterations converge faster than traditional Krasnoselskii–Mann iterations.