发表机构
Nara Institute of Science and Technology; Kyoto University; RIKEN Center for Biosystems Dynamics Research（奈良先端科学技术大学院大学; 京都大学; 理化学研究所生命机能动态研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出基于张量分解的代理建模方法，通过约束多项式优化和T-范数惩罚项整合可行性信息，在合成与真实基准上提升离散黑箱优化的样本效率。
AI 中文摘要
离散黑箱优化通常采用诸如序贯基于模型的优化（SMBO）等方法来解决，该方法通过拟合代理模型来近似离散搜索空间中的昂贵目标函数，以提高样本效率。在许多实际问题中，可行输入集通常由预先已知的逻辑约束给出。然而，现有的代理建模技术通常无法捕捉离散输入空间中控制可行性的符号规则。在本文中，我们提出了一种基于张量分解的代理建模方法，该方法在直接整合可行性信息的同时，捕捉离散搜索空间的结构。为实现该方法，我们将代理模型训练表述为一个约束多项式优化问题，并使用由T-范数导出的可微惩罚项来求解其松弛形式。我们在合成基准和真实世界基准（包括一个压力容器设计任务）上的实验表明，所提出的方法通过有效引导搜索远离不可行区域，提高了样本效率。
英文摘要
Discrete black-box optimization is often addressed using approaches such as Sequential Model-Based Optimization (SMBO), which aims to improve sample efficiency by fitting surrogate models that approximate a costly objective function over a discrete search space. In many real-world problems, the set of feasible inputs is often given by logical constraints known in advance. However, existing surrogate modeling techniques generally fail to capture the symbolic rules governing feasibility in discrete input spaces. In this paper, we propose a surrogate modeling approach based on tensor decomposition that captures the structure of discrete search spaces while directly integrating feasibility information. To implement this approach, we formulate surrogate model training as a constrained polynomial optimization problem and solve a relaxed formulation using a differentiable penalty term derived from T-norms. Our experiments on both synthetic and real-world benchmarks, including a pressure vessel design task, demonstrate that the proposed method improves sample efficiency by effectively guiding the search away from infeasible regions.
Comments32 pages, including supplementary material. ECML PKDD 2026
Journal refMachine Learning and Knowledge Discovery in Databases. Research Track (ECML PKDD 2026), LNCS 16944, pp. 616-634 (2027)
DOI：10.1007/978-3-032-37667-1_35
