Constrained optimization of objective functions determined from random forests

In this paper, we examine a data-driven optimization approach to making optimal decisions as evaluated by trained random forest, where these can be constrained an arbitrary polyhedral set. We model problem mixed-integer linear program. show solved optimality efficiently using pareto-optimal Benders cuts for ensembles containing modest number of trees. consider forest approximation that consists sampling subset trees and establish gives rise near-optimal solutions proving analytical guarantees. particular, axis-aligned trees, the need sample is sublinear in size being approximated. Motivated result, propose heuristics inspired cross-validation optimize over smaller forests rather than one large assess their performance on synthetic datasets. present two case studies property investment jury selection problem. performs well against other benchmarks while providing insights into sensitivity algorithm's different parameters forest.