A Reciprocity Between Tree Ensemble Optimization and Multilinear Optimization
建立了树集成函数优化与多线性函数优化之间的多项式规模转化，从而为树集成优化问题推导出更强的数学规划形式，并为多线性集合的凸包描述提供了新框架。
Capitalizing on the relationships between tree ensembles and multilinear functions Tree ensembles are machine learning models used for regression and classification that combine the predictions of multiple trees. When such trained models are embedded into optimization models in the form of constraints or objectives, a key question is that of deriving best integer programming formulations for them. In “A Reciprocity Between Tree Ensemble Optimization and Multilinear Optimization,” J. Kim, J.-P. Richard, and M. Tawarmalani establish a polynomial-size reduction between the optimization of functions expressed as tree ensembles and the optimization of multilinear functions over a Cartesian product of simplices. This bidirectional reduction permits the derivation of new stronger formulations for tree ensemble optimization problems, including ideal formulations for single trees. It also provides a new framework for the construction of polynomially-sized convex hull descriptions for certain multilinear sets, which permits the generalization of many results from the literature.