Optimization under rare events: scaling laws for linear chance-constrained programs

Autor:	Blanchet, Jose, Jorritsma, Joost, Zwart, Bert
Rok vydání:	2024
Předmět:	Mathematics - Optimization and Control Mathematics - Probability 90C15 (primary) 60F10 60G70 (secondary)
Druh dokumentu:	Working Paper
Popis:	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 also use our results to show that the popular CVaR approximation is asymptotically optimal under light-tail assumptions, but it is sub-optimal in a heavy-tailed setting. Then, we apply point process techniques and random set theory to study the suboptimality gap in the Monte Carlo based scenario approach. Comment: 17 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2407.11825 Zobrazit plný text záznamu View this record from Arxiv