mlsanityData to 7 Oct 2026

Local Constrained Bayesian Optimization

arXiv 2603.07965 ↗First posted 9 Mar 2026stat.ML cs.LGcited by 0

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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.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 30 of its 52 references that are in the map. First posted on arXiv 9 Mar 2026.

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30 of 52 references.

References · 30

  1. 2019Scalable Global Optimization via Local Bayesian Optimizationcited by 359
  2. 2017Safe Model-based Reinforcement Learning with Stability Guaranteescited by 347
  3. 2021High-Dimensional Bayesian Optimization with Sparse Axis-Aligned Subspacescited by 139
  4. 2015High Dimensional Bayesian Optimisation and Bandits via Additive Modelscited by 137
  5. 2020Scalable Constrained Bayesian Optimizationcited by 84
  6. 2018Stagewise Safe Bayesian Optimization with Gaussian Processescited by 79
  7. 2019Adaptive and Safe Bayesian Optimization in High Dimensions via One-Dimensional Subspacescited by 73
  8. 2015Predictive Entropy Search for Bayesian Optimization with Unknown Constraintscited by 51
  9. 2022Constrained Efficient Global Optimization of Expensive Black-box Functionscited by 49
  10. 2021Local policy search with Bayesian optimizationcited by 37
  11. 2016Bayesian optimization under mixed constraints with a slack-variable augmented Lagrangiancited by 29
  12. 2019An Inexact Augmented Lagrangian Framework for Nonconvex Optimization with Nonlinear Constraintscited by 29
18 more
  1. 2022Local Bayesian optimization via maximizing probability of descentcited by 29
  2. 2021TREGO: a Trust-Region Framework for Efficient Global Optimizationcited by 28
  3. 2021Sequential- and Parallel- Constrained Max-value Entropy Search via Information Lower Boundcited by 23
  4. 2022On Kernelized Multi-Armed Bandits with Constraintscited by 23
  5. 2020Rate-improved Inexact Augmented Lagrangian Method for Constrained Nonconvex Optimizationcited by 21
  6. 2019Constrained Bayesian Optimization with Max-Value Entropy Searchcited by 20
  7. 2022Stochastic Inexact Augmented Lagrangian Method for Nonconvex Expectation Constrained Optimizationcited by 19
  8. 2023The Behavior and Convergence of Local Bayesian Optimizationcited by 19
  9. 2023Complexity of Single Loop Algorithms for Nonlinear Programming with Stochastic Objective and Constraintscited by 16
  10. 2024Variance-reduced first-order methods for deterministically constrained stochastic nonconvex optimization with strong convergence guaranteescited by 11
  11. 2021Bayesian Optimisation for Constrained Problemscited by 9
  12. 2022Rectified Pessimistic-Optimistic Learning for Stochastic Continuum-armed Bandit with Constraintscited by 9
  13. 2024Minimizing UCB: a Better Local Search Strategy in Local Bayesian Optimizationcited by 9
  14. 2025NeST-BO: Fast Local Bayesian Optimization via Newton-Step Targeting of Gradient and Hessian Informationcited by 6
  15. 2026BayeSQP: Bayesian Optimization through Sequential Quadratic Programmingcited by 5
  16. 2024Safe Bayesian Optimization for the Control of High-Dimensional Embodied Systemscited by 4
  17. 2023Primal-Dual Contextual Bayesian Optimization for Control System Online Optimization with Time-Average Constraintscited by 3
  18. 2025Convergence Rates of Constrained Expected Improvementcited by 2

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