Stochastic Proximal Point Methods for Monotone Inclusions Under Expected Similarity

Abstract

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.

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Cite

Text

Sadiev et al. "Stochastic Proximal Point Methods for Monotone Inclusions Under Expected Similarity." NeurIPS 2024 Workshops: OPT, 2024.

Markdown

[Sadiev et al. "Stochastic Proximal Point Methods for Monotone Inclusions Under Expected Similarity." NeurIPS 2024 Workshops: OPT, 2024.](https://mlanthology.org/neuripsw/2024/sadiev2024neuripsw-stochastic/)

BibTeX

@inproceedings{sadiev2024neuripsw-stochastic,
  title     = {{Stochastic Proximal Point Methods for Monotone Inclusions Under Expected Similarity}},
  author    = {Sadiev, Abdurakhmon and Condat, Laurent and Richtárik, Peter},
  booktitle = {NeurIPS 2024 Workshops: OPT},
  year      = {2024},
  url       = {https://mlanthology.org/neuripsw/2024/sadiev2024neuripsw-stochastic/}
}