In this paper, we establish a polynomial equivalence between tree ensemble optimization and optimization of multilinear functions over the Cartesian product of simplices. We use this insight to derive new formulations for tree ensemble optimization problems and to obtain new convex hull results for multilinear polytopes. A computational experiment on multi-commodity transportation problems with costs modeled using tree ensembles shows the practical advantage of our formulation relative to existing formulations of tree ensembles and other piecewise-linear modeling techniques. Motivated by the inability of tree ensembles to model multilinear functions of continuous variables, we then propose a generalization of decision-trees and provide empirical evidence of a better out-of-sample fit for a large collection of randomly perturbed nonlinear functions.
View A Reciprocity Between Tree Ensemble Optimization and Multilinear Optimization