Distributionally Robust Optimization with Moment Ambiguity Sets
نویسندگان
چکیده
Abstract This paper studies distributionally robust optimization (DRO) when the ambiguity set is given by moments for distributions. The objective and constraints are polynomials in decision variables. We reformulate DRO with equivalent moment conic constraints. Under some general assumptions, we prove to a linear problem psd polynomial cones. A Moment-SOS relaxation method proposed solve it. Its asymptotic finite convergence shown under certain assumptions. Numerical examples presented show how problems.
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 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 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 کاملDistributionally Robust Reward-Risk Ratio Optimization with Moment Constraints
Reward-risk ratio optimization is an important mathematical approach in finance. We revisit the model by considering a situation where an investor does not have complete information on the distribution of the underlying uncertainty and consequently a robust action is taken to mitigate the risk arising from ambiguity of the true distribution. We consider a distributionally robust reward-risk rat...
متن کاملQuantitative Stability Analysis for Distributionally Robust Optimization with Moment Constraints
In this paper we consider a broad class of distributionally robust optimization (DRO for short) problems where the probability of the underlying random variables depends on the decision variables and the ambiguity set is defined through parametric moment conditions with generic cone constraints. Under some moderate conditions including Slater type conditions of cone constrained moment system an...
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: Journal of Scientific Computing
سال: 2022
ISSN: ['1573-7691', '0885-7474']
DOI: https://doi.org/10.1007/s10915-022-02063-8