arXiv:2606. 11773v1 Announce Type: cross Abstract: Optimistic Gradient Descent Ascent (OGDA) and Optimistic Multiplicative-Weights Update (OMWU) are two very popular algorithms to solve convex/concave saddle-point problems, where OMWU is the non-Euclidean, entropic version of OGDA.
By Francesco Orabona
arXiv:2602. 21436v2 Announce Type: replace-cross Abstract: In this paper, we study last-iterate convergence of learning algorithms in bilinear saddle-point problems, a preferable notion of convergence that captures the day-to-day behavior of learning dynamics.
By Arnab Maiti, Claire Jie Zhang, Kevin Jamieson, Jamie Heather Morgenstern, Ioannis Panageas, Lillian J. Ratliff
arXiv:2503. 04712v3 Announce Type: replace-cross Abstract: We study the optimization of non-convex functions that are not necessarily smooth (gradient and/or Hessian are Lipschitz) using first order methods.
By Daniel Yiming Cao, August Y. Chen, Karthik Sridharan, Benjamin Tang
arXiv:2606. 11431v1 Announce Type: new Abstract: Mirror Descent (MD) extends Gradient Descent (GD) beyond Euclidean geometry and has recently reappeared as a lens for KL-regularized policy optimization in reinforcement learning and LLM post-training.
By Shira Vansover-Hager, Matan Schliserman, Ofir Schlisselberg, Tomer Koren
arXiv:2609. 13646v1 Announce Type: new Abstract: This work addresses decentralized online Riemannian optimization on Hadamard manifolds.
By Zhanyuan Cai, Emre Sahinoglu, Shahin Shahrampour
The limited-memory BFGS (L-BFGS) algorithm is a cornerstone of large-scale optimization due to its linear memory and computational costs. However, in ill-conditioned or non-convex landscapes, the implicit inverse Hessian approximation can suffer from an exploding condition number, leading to numerical instability and degraded convergence.