Gradient boosted trees and other regression tree models perform well in a wide range of real-world, industrial applications. These tree models (i) offer insight into important prediction features, (ii) effectively manage sparse data, and (iii) have excellent prediction capabilities. Despite their advantages, they are generally unpopular for decision-making tasks and black-box optimization, which is due to their difficult-to-optimize structure and the lack of a reliable uncertainty measure. ENTMOOT is our new framework for integrating (already trained) tree models into larger optimization problems. The contributions of ENTMOOT include: (i) explicitly introducing a reliable uncertainty measure that is compatible with tree models, (ii) solving the larger optimization problems that incorporate these uncertainty aware tree models, (iii) proving that the solutions are globally optimal, i.e. no better solution exists. In particular, we show how the ENTMOOT approach allows a simple integration of tree models into decision-making and black-box optimization, where it proves as a strong competitor to commonly-used frameworks.

梯度增强树和其他回归树模型在各种实际的工业应用中表现良好。这些树模型（i）提供对重要预测功能的洞察力；（ii）有效管理稀疏数据；（iii）具有出色的预测能力。尽管它们具有优势，但由于其难以优化的结构以及缺乏可靠的不确定性度量，它们通常在决策任务和黑匣子优化方面并不受欢迎。ENTMOOT是我们的新框架，用于将（已经训练有素的）树模型集成到较大的优化问题中。ENTMOOT的贡献包括：（i）明确引入与树模型兼容的可靠不确定性度量；（ii）解决包含这些具有不确定性的树模型的较大优化问题；（iii）证明解是全局最优的，即不存在更好的解。特别是，我们展示了ENTMOOT方法如何允许将树模型简单地集成到决策和黑盒优化中，在实践中它被证明是常用框架的有力竞争者。