Consistency of Distributionally Robust Risk- and Chance-Constrained Optimization Under Wasserstein Ambiguity Sets
نویسندگان
چکیده
We study stochastic optimization problems with chance and risk constraints, where in the latter, is quantified terms of conditional value-at-risk (CVaR). consider distributionally robust versions these problems, constraints are required to hold for a family distributions constructed from observed realizations uncertainty via Wasserstein distance. Our main results establish that if samples drawn independently an underlying distribution satisfy suitable technical assumptions, then optimal value optimizers converge respective quantities original as sample size increases.
منابع مشابه
Distributionally Robust Optimization with Infinitely Constrained Ambiguity Sets
We consider a distributionally robust optimization problem where the ambiguity set of probability distributions is characterized by a tractable conic representable support set and expectation constraints. Specifically, we propose and motivate a new class of infinitely constrained ambiguity sets in which the number of expectation constraints could potentially be infinite. We show how the infinit...
متن کاملDistributionally robust chance-constrained linear programs
In this paper, we discuss linear programs in which the data that specify the constraints are subject to random uncertainty. A usual approach in this setting is to enforce the constraints up to a given level of probability. We show that for a wide class of probability distributions (i.e. radial distributions) on the data, the probability constraints can be explicitly converted into convex second...
متن کاملNear-Optimal Bayesian Ambiguity Sets for Distributionally Robust Optimization
We propose a Bayesian framework for assessing the relative strengths of data-driven ambiguity sets in distributionally robust optimization (DRO) when the underlying distribution is defined by a finite-dimensional parameter. The key idea is to measure the relative size between a candidate ambiguity set and a specific, asymptotically optimal set. This asymptotically optimal set is provably the sm...
متن کاملOn Distributionally Robust Chance-Constrained Linear Programs1
In this paper, we discuss linear programs in which the data that specify the constraints are subject to random uncertainty. A usual approach in this setting is to enforce the constraints up to a given level of probability. We show that, for a wide class of probability distributions (namely, radial distributions) on the data, the probability constraints can be converted explicitly into convex se...
متن کاملNear-Optimal Ambiguity Sets for Distributionally Robust Optimization
We propose a novel, Bayesian framework for assessing the relative strengths of data-driven ambiguity sets in distributionally robust optimization (DRO). The key idea is to measure the relative size between a candidate ambiguity set and an asymptotically optimal set as the amount of data grows large. This asymptotically optimal set is provably the smallest convex ambiguity set that satisfies a s...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: IEEE Control Systems Letters
سال: 2021
ISSN: ['2475-1456']
DOI: https://doi.org/10.1109/lcsys.2020.3043228