# Local Constrained Bayesian Optimization

arXiv: https://arxiv.org/abs/2603.07965 · HTML: https://mlsanity.com/paper/2603.07965/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 30 of its 52 references that are in the map.
- First posted on arXiv 9 Mar 2026.

## Builds on (most cited first, 30 of 30)

- [Scalable Global Optimization via Local Bayesian Optimization](https://mlsanity.com/paper/1910.01739/) (2019)
- [Safe Model-based Reinforcement Learning with Stability Guarantees](https://mlsanity.com/paper/1705.08551/) (2017)
- [High-Dimensional Bayesian Optimization with Sparse Axis-Aligned Subspaces](https://mlsanity.com/paper/2103.00349/) (2021)
- [High Dimensional Bayesian Optimisation and Bandits via Additive Models](https://mlsanity.com/paper/1503.01673/) (2015)
- [Scalable Constrained Bayesian Optimization](https://mlsanity.com/paper/2002.08526/) (2020)
- [Stagewise Safe Bayesian Optimization with Gaussian Processes](https://mlsanity.com/paper/1806.07555/) (2018)
- [Adaptive and Safe Bayesian Optimization in High Dimensions via One-Dimensional Subspaces](https://mlsanity.com/paper/1902.03229/) (2019)
- [Predictive Entropy Search for Bayesian Optimization with Unknown Constraints](https://mlsanity.com/paper/1502.05312/) (2015)
- [Constrained Efficient Global Optimization of Expensive Black-box Functions](https://mlsanity.com/paper/2211.00162/) (2022)
- [Local policy search with Bayesian optimization](https://mlsanity.com/paper/2106.11899/) (2021)
- [Local Bayesian optimization via maximizing probability of descent](https://mlsanity.com/paper/2210.11662/) (2022)
- [Bayesian optimization under mixed constraints with a slack-variable augmented Lagrangian](https://mlsanity.com/paper/1605.09466/) (2016)
- [An Inexact Augmented Lagrangian Framework for Nonconvex Optimization with Nonlinear Constraints](https://mlsanity.com/paper/1906.11357/) (2019)
- [TREGO: a Trust-Region Framework for Efficient Global Optimization](https://mlsanity.com/paper/2101.06808/) (2021)
- [Sequential- and Parallel- Constrained Max-value Entropy Search via Information Lower Bound](https://mlsanity.com/paper/2102.09788/) (2021)
- [On Kernelized Multi-Armed Bandits with Constraints](https://mlsanity.com/paper/2203.15589/) (2022)
- [Rate-improved Inexact Augmented Lagrangian Method for Constrained Nonconvex Optimization](https://mlsanity.com/paper/2007.01284/) (2020)
- [Constrained Bayesian Optimization with Max-Value Entropy Search](https://mlsanity.com/paper/1910.07003/) (2019)
- [The Behavior and Convergence of Local Bayesian Optimization](https://mlsanity.com/paper/2305.15572/) (2023)
- [Stochastic Inexact Augmented Lagrangian Method for Nonconvex Expectation Constrained Optimization](https://mlsanity.com/paper/2212.09513/) (2022)
- [Complexity of Single Loop Algorithms for Nonlinear Programming with Stochastic Objective and Constraints](https://mlsanity.com/paper/2311.00678/) (2023)
- [Variance-reduced first-order methods for deterministically constrained stochastic nonconvex optimization with strong convergence guarantees](https://mlsanity.com/paper/2409.09906/) (2024)
- [Bayesian Optimisation for Constrained Problems](https://mlsanity.com/paper/2105.13245/) (2021)
- [Rectified Pessimistic-Optimistic Learning for Stochastic Continuum-armed Bandit with Constraints](https://mlsanity.com/paper/2211.14720/) (2022)
- [Minimizing UCB: a Better Local Search Strategy in Local Bayesian Optimization](https://mlsanity.com/paper/2405.15285/) (2024)
- [NeST-BO: Fast Local Bayesian Optimization via Newton-Step Targeting of Gradient and Hessian Information](https://mlsanity.com/paper/2510.05516/) (2025)
- [BayeSQP: Bayesian Optimization through Sequential Quadratic Programming](https://mlsanity.com/paper/2602.03232/) (2026)
- [Safe Bayesian Optimization for the Control of High-Dimensional Embodied Systems](https://mlsanity.com/paper/2412.20350/) (2024)
- [Primal-Dual Contextual Bayesian Optimization for Control System Online Optimization with Time-Average Constraints](https://mlsanity.com/paper/2304.06104/) (2023)
- [Convergence Rates of Constrained Expected Improvement](https://mlsanity.com/paper/2505.11323/) (2025)

## Abstract (arXiv)

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.