Variance-Reduced Fast Krasnoselkii-Mann Methods for Finite-Sum Root-Finding Problems
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arXiv:2609. 28543v1 Announce Type: cross Abstract: We analyze a simple stochastic inertial Krasnosel'skii--Mann (iKM) method for finding a fixed point of a nonexpansive operator in a real Hilbert space.
arXiv:2608. 12043v1 Announce Type: cross Abstract: Acceleration for deterministic root-finding problems has been extensively studied in recent years; specifically, the anchor-based, or Halpern-type methods achieve optimal convergence rates with respect to the operator norm.
arXiv:2502.21099v3 Announce Type: replace-cross Abstract: This paper proposes {\sf AEPG-SPIDER}, an Adaptive Extrapolated Proximal Gradient (AEPG) method with variance reduction for minimizing compos...
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.
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...
arXiv:2603.15576v2 Announce Type: replace-cross Abstract: This paper develops new variance-reduction techniques for the forward-reflected-backward splitting (FRBS) method to solve a class of possibly...