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arXiv · 2603.07965

Local Constrained Bayesian Optimization

Jing Jingzhe·Fan Zheyi·Szu Hui Ng·Qingpei Hu
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Abstract

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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Jing Jingzhe, Fan Zheyi, Szu Hui Ng, Qingpei Hu. 2026-07-03. Local Constrained Bayesian Optimization. https://arxiv.org/abs/2603.07965

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