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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2506.11409 |
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| _version_ | 1866913890999205888 |
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| author | Tao, Haochen Iannelli, Andrea Marschner, Meggie Staudigl, Mathias Shanbhag, Uday V. Cui, Shisheng |
| author_facet | Tao, Haochen Iannelli, Andrea Marschner, Meggie Staudigl, Mathias Shanbhag, Uday V. Cui, Shisheng |
| contents | In this paper, we address \ac{SGNEP} seeking with risk-neutral agents. Our main contribution lies the development of a stochastic variance-reduced gradient (SVRG) technique, modified to contend with general sample spaces, within a stochastic forward-backward-forward splitting scheme for resolving structured monotone inclusion problems. This stochastic scheme is a double-loop method, in which the mini-batch gradient estimator is computed periodically in the outer loop, while only cheap sampling is required in a frequently activated inner loop, thus achieving significant speed-ups when sampling costs cannot be overlooked. The algorithm is fully distributed and it guarantees almost sure convergence under appropriate batch size and strong monotonicity assumptions. Moreover, it exhibits a linear rate with possible biased estimators, which is rather mild and imposed in many simulation-based optimization schemes. Under monotone regimes, the expectation of the gap function of an averaged iterate diminishes at a suitable sublinear rate while the sample-complexity of computing an $ε$-solution is provably $\mathcal{O}(ε^{-3})$. A numerical study on a class of networked Cournot games reflects the performance of our proposed algorithm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_11409 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Complexity guarantees for risk-neutral generalized Nash equilibrium problems Tao, Haochen Iannelli, Andrea Marschner, Meggie Staudigl, Mathias Shanbhag, Uday V. Cui, Shisheng Optimization and Control In this paper, we address \ac{SGNEP} seeking with risk-neutral agents. Our main contribution lies the development of a stochastic variance-reduced gradient (SVRG) technique, modified to contend with general sample spaces, within a stochastic forward-backward-forward splitting scheme for resolving structured monotone inclusion problems. This stochastic scheme is a double-loop method, in which the mini-batch gradient estimator is computed periodically in the outer loop, while only cheap sampling is required in a frequently activated inner loop, thus achieving significant speed-ups when sampling costs cannot be overlooked. The algorithm is fully distributed and it guarantees almost sure convergence under appropriate batch size and strong monotonicity assumptions. Moreover, it exhibits a linear rate with possible biased estimators, which is rather mild and imposed in many simulation-based optimization schemes. Under monotone regimes, the expectation of the gap function of an averaged iterate diminishes at a suitable sublinear rate while the sample-complexity of computing an $ε$-solution is provably $\mathcal{O}(ε^{-3})$. A numerical study on a class of networked Cournot games reflects the performance of our proposed algorithm. |
| title | Complexity guarantees for risk-neutral generalized Nash equilibrium problems |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2506.11409 |