# Stochastic Proximal Point Methods for Monotone Inclusions under Expected Similarity

arXiv: https://arxiv.org/abs/2405.14255 · HTML: https://mlsanity.com/paper/2405.14255/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 May 2024.

## Built on by (most cited first, 3 of 3)

- [Tighter Performance Theory of FedExProx](https://mlsanity.com/paper/2410.15368/) (2024)
- [Mean-square and sublinear convergence of a stochastic proximal point algorithm in metric spaces of nonpositive curvature](https://mlsanity.com/paper/2510.10697/) (2025)
- [Dual-Anchor Acceleration Is Near-Optimal for Stochastic Monotone Root-Finding](https://mlsanity.com/paper/2609.36033/) (2026)

## Abstract (arXiv)

Monotone inclusions have a wide range of applications, including minimization, saddle-point, and equilibria problems. We introduce new stochastic algorithms, with or without variance reduction, to estimate a root of the expectation of possibly set-valued monotone operators, using at every iteration one call to the resolvent of a randomly sampled operator. We also introduce a notion of similarity between the operators, which holds even for discontinuous operators. We leverage it to derive linear convergence results in the strongly monotone setting.