joint work with Angelos Georghiou, Phebe Vayanos
We consider two-stage robust optimization problems in which the first stage variables decide on the uncertain parameters that will be observed between the first and the second decision stages. The information available in the second stage is thus decision-dependent and can be discovered by making strategic exploratory investments in the first stage. We propose a novel min-max-min-max formulation of the problem. We prove the correctness of this formulation and leverage this new model to provide a solution method inspired from the K-adaptability approximation approach.
joint work with Daniel Kuhn, Peyman Mohajerin Esfahani
We introduce a distributionally robust maximum likelihood estimation model with a Wasserstein ambiguity set to infer the inverse covariance matrix of a p-dimensional Gaussian random vector from n independent samples. We show that the estimation problem has an analytical solution that is interpreted as a nonlinear shrinkage estimator. Besides being invertible and well-conditioned, the new shrinkage estimator is rotation-equivariant and preserves the order of the eigenvalues of the sample covariance matrix.
joint work with Angelos Tsoukalas, Wolfram Wiesemann
In this talk, we discuss convergent hierarchies of primal (conservative) and dual (progressive) bounds for two-stage robust optimization problems that trade off the competing goals of tractability and optimality: While the coarsest bounds recover a tractable but suboptimal affine decision rule of the two-stage robust optimization problem, the refined bounds lift extreme points of the uncertainty set until an exact but intractable extreme point reformulation of the problem is obtained.