Constrained optimization of objective functions determined from random forests
研究如何用混合整数线性规划方法，在随机森林评估下做出受约束的最优决策，并证明通过采样少量树可得到近似最优解，适用于投资和陪审团选择等场景。
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.