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. It is known since the '80s that the last iterate of OGDA asymptotically converges to a saddle point in smooth problems.
arXiv:2603. 10485v3 Announce Type: replace-cross Abstract: In this work, we study the convergence properties of the Dual Space Preconditioned Gradient Descent, encompassing optimizers such as Normalized Gradient Descent and Gradient Clipping.
By Reza Ghane, Danil Akhtiamov, Babak Hassibi
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:2605. 18694v2 Announce Type: replace-cross Abstract: Many tasks in modern machine learning are observed to involve heavy-tailed gradient noise during the optimization process.
By Zijian Liu
arXiv:2608. 04382v1 Announce Type: new Abstract: Gradient descent has been of particular interest in modern machine learning beyond sole focus on optimization.
By Han Bao
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