Learning in Inverse Optimization: Incenter Cost, Augmented Suboptimality Loss, and Algorithms

In Inverse Optimization (IO), an expert agent solves an optimization problem parametric in an exogenous signal. From a learning perspective, the goal is to learn the expert’s cost function given a dataset of signals and corresponding optimal actions. Motivated by the geometry of the IO set of consistent cost vectors, we introduce the “incenter” concept, … Read more

Hidden convexity in a class of optimization problems with bilinear terms

In this paper we identify a new class of nonconvex optimization problems that can be equivalently reformulated to convex ones. These nonconvex problems can be characterized by convex functions with bilinear arguments. We describe several examples of important applications that have this structure. A reformulation technique is presented which converts the problems in this class … Read more