Optimization under rare events: scaling laws for linear chance-constrained programs
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912699895513088 |
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| author | Blanchet, Jose Jorritsma, Joost Zwart, Bert |
| author_facet | Blanchet, Jose Jorritsma, Joost Zwart, Bert |
| contents | We consider a class of chance-constrained programs in which profit needs to be maximized while enforcing that a given adverse event remains rare. Using techniques from large deviations and extreme value theory, we show how the optimal value scales as the prescribed bound on the violation probability becomes small and how convex programs emerge in the limit. We use our results to analyze the performance of existing popular approaches in the rare-event regime. We show that the popular CVaR and sample approximations have optimality properties under light-tailed assumptions on the randomness, while they behave sub-optimal in a heavy-tailed setting. Our results are derived using large deviations theory, extreme value theory, process techniques, and random set theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_11825 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimization under rare events: scaling laws for linear chance-constrained programs Blanchet, Jose Jorritsma, Joost Zwart, Bert Optimization and Control Probability 90C15 (primary), 60F10, 60G70 (secondary) We consider a class of chance-constrained programs in which profit needs to be maximized while enforcing that a given adverse event remains rare. Using techniques from large deviations and extreme value theory, we show how the optimal value scales as the prescribed bound on the violation probability becomes small and how convex programs emerge in the limit. We use our results to analyze the performance of existing popular approaches in the rare-event regime. We show that the popular CVaR and sample approximations have optimality properties under light-tailed assumptions on the randomness, while they behave sub-optimal in a heavy-tailed setting. Our results are derived using large deviations theory, extreme value theory, process techniques, and random set theory. |
| title | Optimization under rare events: scaling laws for linear chance-constrained programs |
| topic | Optimization and Control Probability 90C15 (primary), 60F10, 60G70 (secondary) |
| url | https://arxiv.org/abs/2407.11825 |