Stochastic Proximal Point Methods for Monotone Inclusions under Expected Similarity
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913359716155392 |
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| author | Sadiev, Abdurakhmon Condat, Laurent Richtárik, Peter |
| author_facet | Sadiev, Abdurakhmon Condat, Laurent Richtárik, Peter |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_14255 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stochastic Proximal Point Methods for Monotone Inclusions under Expected Similarity Sadiev, Abdurakhmon Condat, Laurent Richtárik, Peter Optimization and Control 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. |
| title | Stochastic Proximal Point Methods for Monotone Inclusions under Expected Similarity |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2405.14255 |