mlsanityData to 7 Oct 2026

Bayesian optimization under mixed constraints with a slack-variable augmented Lagrangian

arXiv 1605.09466 ↗First posted 31 May 2016stat.CO stat.MLcited by 29

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Abstract (arXiv)

An augmented Lagrangian (AL) can convert a constrained optimization problem into a sequence of simpler (e.g., unconstrained) problems, which are then usually solved with local solvers. Recently, surrogate-based Bayesian optimization (BO) sub-solvers have been successfully deployed in the AL framework for a more global search in the presence of inequality constraints; however, a drawback was that expected improvement (EI) evaluations relied on Monte Carlo. Here we introduce an alternative slack variable AL, and show that in this formulation the EI may be evaluated with library routines. The slack variables furthermore facilitate equality as well as inequality constraints, and mixtures thereof. We show how our new slack "ALBO" compares favorably to the original. Its superiority over conventional alternatives is reinforced on several mixed constraint examples.

Key facts. Cited by 29 papers in the map (data through 7 Oct 2026). First posted on arXiv 31 May 2016.

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Citing papers per year: 2021: 9; 2022: 2; 2023: 5; 2024: 2; 2025: 6; 2026: 5.

29 papers.

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  2. 2021OpenBox: A Generalized Black-box Optimization Servicecited by 46
  3. 2021TREGO: a Trust-Region Framework for Efficient Global Optimizationcited by 28
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  5. 2024Bayesian optimization as a flexible and efficient design framework for sustainable process systemscited by 15
  6. 2022A Bayesian Optimization Framework for Finding Local Optima in Expensive Multi-Modal Functionscited by 12
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  8. 2021Bayesian Optimisation for Constrained Problemscited by 9
  9. 2021A comparison of mixed-variables Bayesian optimization approachescited by 6
  10. 2023No-Regret Constrained Bayesian Optimization of Noisy and Expensive Hybrid Models using Differentiable Quantile Function Approximationscited by 6
  11. 2023Constrained Causal Bayesian Optimizationcited by 6
  12. 2023Constrained Bayesian Optimization Under Partial Observations: Balanced Improvements and Provable Convergencecited by 6
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  2. 2026BayeSQP: Bayesian Optimization through Sequential Quadratic Programmingcited by 5
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  4. 2025Feasibility-Driven Trust Region Bayesian Optimizationcited by 4
  5. 2025Posterior Inference in Latent Space for Scalable Constrained Black-box Optimizationcited by 4
  6. 2021A New Knowledge Gradient-based Method for Constrained Bayesian Optimizationcited by 2
  7. 2023Soft Actor-Critic Algorithm with Truly-satisfied Inequality Constraintcited by 2
  8. 2023Constrained Bayesian Optimization with Adaptive Active Learning of Unknown Constraintscited by 2
  9. 2025Convergence Rates of Constrained Expected Improvementcited by 2
  10. 2021Fast Design Space Exploration of Nonlinear Systems: Part Icited by 1
  11. 2025ACE: Adapting sampling for Counterfactual Explanationscited by 0
  12. 2025A Constrained Multi-Fidelity Bayesian Optimization Methodcited by 0
  13. 2025Gaussian Process Assisted Meta-learning for Image Classification and Object Detection Modelscited by 0
  14. 2026Local Constrained Bayesian Optimizationcited by 0
  15. 2026Exploiting Separability in Multi-Scale Grey-Box Bayesian Optimizationcited by 0
  16. 2026Constraint-Aware Discrete Black-Box Optimization Using Tensor Decompositioncited by 0
  17. 2026Converge Then Diversify: Decoupling Convergence and Diversity in Multi-Objective Bayesian Optimisationcited by 0