ILP-BO：基于整数线性规划的黑箱优化
ILP-BO: Integer Linear Programming-Based Black-Box Optimization
AI总结：
提出ILP-BO，一种将离散域黑箱优化转化为整数线性规划问题的准贝叶斯优化框架，通过精确表示核函数并引入汉明距离边际，实现全局最优候选选择，在基准测试中性能与贝叶斯优化相当。
AI中文摘要：
黑箱优化（BO）是一个强大的框架，用于在有限评估次数内优化昂贵的目标函数或未知函数。标准黑箱优化（如贝叶斯优化）的核心步骤是优化基于代理模型的采集准则，通常使用非线性优化或启发式搜索来执行。因此，传统黑箱优化通常无法保证候选选择中的全局最优性。在本研究中，我们提出了基于整数线性规划的黑箱优化（ILP-BO），这是一种准贝叶斯优化框架，将离散域上基于核的代理优化转化为整数线性规划（ILP）问题。关键思想是通过引入二值独热辅助变量，在有限离散距离水平上精确表示非线性核函数。这种转化将非线性代理模型转换为具有线性约束和二值变量的线性目标。为了在保持线性结构的同时纳入探索，我们进一步引入了汉明距离边际，该边际排除先前观测点周围的邻域。我们为几种标准核函数推导了所提出的公式，并基于二值搜索空间中的测度获得了汉明距离阈值的解析上界。由此产生的候选选择问题可以通过整数规划求解器求解，并带有最优性证书。因此，我们的方法有潜力成为一个高度透明的黑箱优化框架。在合成和离散优化基准上的实验表明，与实用的贝叶斯优化方法相比，ILP-BO实现了有竞争力的优化性能。
英文摘要：
Black-box Optimization (BO) is a powerful framework for optimizing expensive objective functions or unknown functions with a limited number of evaluations. A central step of standard BO such as Bayesian optimization is the optimization of a surrogate-based acquisition criterion, which is commonly performed using nonlinear optimization or heuristic search. Therefore, conventional black-box optimization generally does not guarantee global optimality in candidate selection. In this study, we propose Integer Linear Programming-based Black-box Optimization (ILP-BO), a quasi-Bayesian optimization framework that transforms kernel-based surrogate optimization over discrete domains into an Integer Linear Programming (ILP) problem. The key idea is to represent nonlinear kernel functions exactly on finite discrete distance levels by introducing binary one-hot auxiliary variables. This transformation converts the nonlinear surrogate into a linear objective with linear constraints and binary variables. To incorporate exploration while preserving the linear structure, we further introduce a Hamming-distance margin that excludes neighborhoods around previously observed points. We derive the proposed formulation for several standard kernels and obtain an analytical upper bound on the Hamming-distance threshold based on the measure in the binary search space. The resulting candidate-selection problem can be solved by integer programming solvers with certificates of optimality. Thus, our methodology has the potential to serve as a highly transparent black-box optimization framework. Experiments on synthetic and discrete optimization benchmarks show that ILP-BO achieves competitive optimization performance compared with practical Bayesian optimization methods.
