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:2609.09524v1 Announce Type: cross
Abstract: We study the oracle complexity of computing a point with small fixed-point residual $\|T(x)-x\| \leq \epsilon$, for a general norm $\|\cdot\|$ and a...
By Jelena Diakonikolas, Crist\'obal Guzm\'an, David Mart\'inez-Rubio
arXiv:2609.36033v1 Announce Type: cross
Abstract: Among distinct optimal acceleration mechanisms for deterministic monotone root-finding problems and fixed-point problems, dual-anchoring has recently...
By TaeHo Yoon, Nicolas Loizou
arXiv:2609.30499v1 Announce Type: new
Abstract: Uniform noise-moment bounds exclude stochastic gradients whose variability increases with the iterate. We study ordinary, single-sample stochastic grad...
By Wei Biao Wu
arXiv:2607. 13414v1 Announce Type: cross Abstract: Non-expansive two-time-scale stochastic approximation is governed by a slow stochastic Krasnoselskii--Mann fixed-point iteration rather than by contraction to a unique equilibrium.
By Dhruv Sarkar, Vaneet Aggarwal
arXiv:2406.02413v4 Announce Type: replace-cross
Abstract: We propose a new class of fast Krasnoselkii--Mann methods with variance reduction to solve a finite-sum co-coercive equation $Gx = 0$. Our al...
By Quoc Tran-Dinh