Randomized quasi-Monte Carlo methods for risk-averse stochastic optimization
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912455024705536 |
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| author | Melnikov, Olena Milz, Johannes |
| author_facet | Melnikov, Olena Milz, Johannes |
| contents | We establish epigraphical and uniform laws of large numbers for sample-based approximations of law invariant risk functionals. These sample-based approximation schemes include Monte Carlo (MC) and certain randomized quasi-Monte Carlo integration (RQMC) methods, such as scrambled net integration. Our results can be applied to the approximation of risk-averse stochastic programs and risk-averse stochastic variational inequalities. Our numerical simulations empirically demonstrate that RQMC approaches based on scrambled Sobol' sequences can yield smaller bias and root mean square error than MC methods for risk-averse optimization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_02842 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Randomized quasi-Monte Carlo methods for risk-averse stochastic optimization Melnikov, Olena Milz, Johannes Optimization and Control 90C15, 90C59, 65C05 We establish epigraphical and uniform laws of large numbers for sample-based approximations of law invariant risk functionals. These sample-based approximation schemes include Monte Carlo (MC) and certain randomized quasi-Monte Carlo integration (RQMC) methods, such as scrambled net integration. Our results can be applied to the approximation of risk-averse stochastic programs and risk-averse stochastic variational inequalities. Our numerical simulations empirically demonstrate that RQMC approaches based on scrambled Sobol' sequences can yield smaller bias and root mean square error than MC methods for risk-averse optimization. |
| title | Randomized quasi-Monte Carlo methods for risk-averse stochastic optimization |
| topic | Optimization and Control 90C15, 90C59, 65C05 |
| url | https://arxiv.org/abs/2408.02842 |