Local Constrained Bayesian Optimization
This work provides a more efficient optimization method for engineers and researchers working with high-dimensional problems under tight or complex constraints, offering a polynomial dependency on dimension where previous methods scaled exponentially.
This paper addresses high-dimensional constrained Bayesian optimization, a problem where existing methods struggle due to the curse of dimensionality. The authors propose Local Constrained Bayesian Optimization (LCBO), which achieves a convergence rate for the Karush-Kuhn-Tucker (KKT) residual that depends polynomially on the dimension $d$, outperforming state-of-the-art baselines on benchmarks up to 100D.
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.