arXiv:2606. 07496v1 Announce Type: new Abstract: Decentralized stochastic optimization is a fundamental paradigm for large-scale learning over networks, where agents communicate only with their neighbors and no central coordinator is required.
By Ming Sun, Kun Yuan
arXiv:2607. 09097v1 Announce Type: cross Abstract: We study stochastic fixed-point equations $\mathbf{T}(\mathbf{x}) = \mathbf{x}$ over normed spaces $(\mathcal{E}, \|\cdot\|)$, where the operator $\mathbf{T}$ is nonexpansive or contractive and is accessed only through unbiased stochastic evaluations with bounded second central moment.
By Jelena Diakonikolas
arXiv:2606. 04757v1 Announce Type: cross Abstract: We study decentralized stochastic smooth convex optimization, where $M$ workers minimize an average objective using local stochastic gradients and neighbor-only communication over a fixed gossip network.
By Nitai Kluger, Amit Attia, Tomer Koren
arXiv:2608. 13467v1 Announce Type: new Abstract: We study the Moreau--Yosida unadjusted Langevin algorithm (MYULA) for the nonsmooth composite target \[ \pi(dx)\propto \exp\{-f(x)-g(x)\}\,dx, \qquad x\in\mathbb R^d, \] where \(f\) is \(m\)-strongly convex with \(L_f\)-Lipschitz gradient and \(g\) is convex and \(G\)-Lipschitz.
By Yuchen Xin, Zhihua Zhang
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: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