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.
By Kuangyu Ding, Kim-Chuan Toh
arXiv:2607. 16384v1 Announce Type: new Abstract: For stochastic gradient descent (SGD) with a constant stepsize $\alpha$, the invariant law of the iterates, centered at a minimizer, describes the behavior of the algorithm over long time horizons.
By Jingyi Zhang, Cheng Mao, Debankur Mukherjee
arXiv:2608. 05460v1 Announce Type: cross Abstract: This work introduces a proximal stochastic subgradient method for minimizing the sum of an expected cost, whose integrand is potentially nonsmooth and nonconvex, and a lower semicontinuous, prox-bounded function.
By Felipe Atenas, Alejandro Jofr\'e, Pedro P\'erez-Aros, David Torregrosa-Bel\'en
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:2606. 28308v1 Announce Type: cross Abstract: Many two-player zero-sum games admit not a unique Nash equilibrium but a convex set of them: a polytope of profiles that all share the minimax value V* yet prescribe different behaviour.
By Luis Leal
arXiv:2606. 04031v1 Announce Type: new Abstract: Coupled gradient descent--where the update of one parameter block depends on another--underlies bilevel optimization, two-time-scale stochastic approximation, and adversarial training.
By Ahanaf Hasan Ariq