Constraint-Aware Discrete Black-Box Optimization Using Tensor Decomposition

arXiv:2609.09370v1 Announce Type: new Abstract: 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.

Abstract: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.

32 pages, including supplementary material. ECML PKDD 2026

Machine Learning (cs.LG)

arXiv:2609.09370 [cs.LG]

(or arXiv:2609.09370v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.09370 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

Machine Learning and Knowledge Discovery in Databases. Research Track (ECML PKDD 2026), LNCS 16944, pp. 616-634 (2027)

https://doi.org/10.1007/978-3-032-37667-1_35 Focus to learn more DOI(s) linking to related resources

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Constraint-Aware Discrete Black-Box Optimization Using Tensor Decomposition

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