针对高维约束优化难题，提出局部约束贝叶斯优化框架
Local Constrained Bayesian Optimization
- 通过可微约束惩罚代理模型，在局部快速下降与不确定性探索间交替
- 在100维基准上显著优于现有方法，收敛速度与维度呈多项式关系
- 适合高维复杂约束场景，如超参数调优或物理仿真设计
高维约束问题的贝叶斯优化仍面临维度诅咒挑战。本文提出局部约束贝叶斯优化（LCBO），专为高维场景设计。不同于易因紧约束提前收缩的信任域方法，LCBO利用约束惩罚代理模型的可微结构，交替执行快速局部下降与基于不确定性的探索。理论上，在温和假设下，对常见核函数，LCBO 的卡鲁什-库恩-塔克（KKT）残差收敛率关于维度 $d$ 呈多项式依赖，提供严格替代全局贝叶斯优化的方案（后者遗憾界通常指数级增长）。在高达100维的基准测试中，LCBO 持续优于当前最优基线。
原文摘要 · Abstract (English)
Bayesian optimization (BO) for high-dimensional constrained problems remains a significant challenge due to the curse of dimensionality. We propose Local Constrained Bayesian Optimization (LCBO), a novel framework tailored for such settings. Unlike trust-region methods that are prone to premature shrinking when confronting tight or complex constraints, LCBO leverages the differentiable landscape of constraint-penalized surrogates to alternate between rapid local descent and uncertainty-driven exploration. Theoretically, we prove that LCBO achieves a convergence rate for the Karush-Kuhn-Tucker (KKT) residual that depends polynomially on the dimension $d$ for common kernels under mild assumptions, offering a rigorous alternative to global BO where regret bounds typically scale exponentially. Extensive evaluations on high-dimensional benchmarks (up to 100D) demonstrate that LCBO consistently outperforms state-of-the-art baselines.
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