Optimizing Objective Functions Determined from Random Forests
Optimizing Objective Functions Determined from Random Forests
复制标题
优化随机森林确定的目标函数
DOI：
10.2139/ssrn.2986630
复制
发表时间：
2017
期刊：
影响因子：
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通讯作者：
G. Perakis
中科院分区：
文献类型：
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作者：
Max Biggs;R. Hariss;G. Perakis
研究了可行决策位于多面体集中的树形集成目标的优化问题。我们将该优化问题建模为混合整数线性规划(MILP)。我们证明了利用帕累托最优折弯割法可以有效地求解该模型的最优解。对于大型问题，我们考虑只由树子集组成的随机森林近似，并通过证明分析保证来分析证明这将导致接近最优解。随着树木数目的增加，近似误差呈指数衰减。受这一结果的启发，我们提出了在较小的森林而不是一个大的森林上进行优化的启发式算法。我们介绍了一个房地产投资问题和一个陪审团选择问题的案例研究。我们证明了这种方法在基准测试中表现良好，同时提供了算法对随机森林不同参数的性能的敏感度的见解。
We study the problem of optimizing a tree-based ensemble objective with the feasible decisions lie in a polyhedral set. We model this optimization problem as a Mixed Integer Linear Program (MILP). We show this model can be solved to optimality efficiently using Pareto optimal Benders cuts. For large problems, we consider a random forest approximation that consists of only a subset of trees and establish analytically that this gives rise to near optimal solutions by proving analytical guarantees. The error of the approximation decays exponentially as the number of trees increases. Motivated from this result, we propose heuristics that optimize over smaller forests rather than one large one. We present case studies on a property investment problem and a jury selection problem. We show this approach performs well against benchmarks, while providing insights into the sensitivity of the algorithm's performance for different parameters of the random forest.