Many distributionally robust optimization (DRO) instances can be formulated as semidefinite programming (SDP) problems. However, SDP problems in practice are computationally challenging. In this talk, we present computationally efficient (inner and outer) approximations for DRO problems based on the idea of the principal component analysis (PCA). We also derive theoretical bounds on the gaps between the original problem and its PCA approximations. Furthermore, an extensive numerical study shows the strength of the proposed approximations in terms of solution quality and runtime.
joint work with Arjun Ramachandra, Karthik Natarajan
Computing tight bounds for the probability of sums of dependent variables is a fundamental problem with several applications. In this work we study the problem of computing the probability of a sum of dependent Bernoulli random variables exceeding k, from a DRO perspective. We study the problem under known univariate and bivariate marginals with tree structure, where a consistent joint distribution is guaranteed to exist. We propose exact and compact linear programming formulations for these sparse forms. This is based on joint work with Arjun Ramachandra and Karthik Natarajan at SUTD.
joint work with Bikramjit Das, Anulekha Dhara
Since the seminal work of Scarf (1958) on the newsvendor problem with ambiguity in the demand distribution, there has been a growing interest in the study of the distributionally robust newsvendor problem. A simple observation shows that the optimal order quantity in Scarf’s model with known first and second moment is also optimal for a heavy-tailed censored student-t distribution with degrees of freedom 2. In this paper, we generalize this “heavy-tail optimality” property of the distributionally robust newsvendor to a more general ambiguity set.