Solving the Optimal Experiment Design Problems with Mixed-Integer Frank-Wolfe-based methods
Abstract.
We tackle the Optimal Experiment Design Problem, which consists in choosing experiments to run or observations to select from a finite set to estimate the parameters of a system. The objective is to maximize some measure of information gained on the system from the observations, leading to a convex integer optimization problem. We leverage Boscia, a recent algorithmic framework, which is based on a nonlinear branch-and-bound with node relaxations solved to approximate optimality using Frank-Wolfe algorithms. One particular advantage of the method is its efficient utilization of the polytope formed by the original constraints which remains preserved by the method, unlike in those relying on epigraph-based formulations. We assess our method against both generic and specialized convex mixed-integer approaches. Computational results highlight the performance of the proposed method, especially on large and challenging instances.
