Constrained optimization of objective functions determined from random forests

Authors: Max Biggs, Rim Hariss and Georgia Perakis

Publication: Production and Operations Management, Forthcoming
First published online: September 2022

Abstract:

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

Desautels 22

In recognition of research excellence as it relates to publications in top-tier management journals, our Faculty has compiled a list of high quality, peer-reviewed management journals, which is referred to as the Desautels 22.