mlsanityData to 7 Oct 2026

BOtied: Multi-objective Bayesian optimization with tied multivariate ranks

arXiv 2306.00344 ↗First posted 1 Jun 2023cs.LG stat.MLcited by 14

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Abstract (arXiv)

Many scientific and industrial applications require the joint optimization of multiple, potentially competing objectives. Multi-objective Bayesian optimization (MOBO) is a sample-efficient framework for identifying Pareto-optimal solutions. At the heart of MOBO is the acquisition function, which determines the next candidate to evaluate by navigating the best compromises among the objectives. In this paper, we show a natural connection between non-dominated solutions and the extreme quantile of the joint cumulative distribution function (CDF). Motivated by this link, we propose the Pareto-compliant CDF indicator and the associated acquisition function, BOtied. BOtied inherits desirable invariance properties of the CDF, and an efficient implementation with copulas allows it to scale to many objectives. Our experiments on a variety of synthetic and real-world problems demonstrate that BOtied outperforms state-of-the-art MOBO acquisition functions while being computationally efficient for many objectives.

Key facts. Cited by 14 papers in the map (data through 7 Oct 2026). Builds on 27 of its 92 references that are in the map. First posted on arXiv 1 Jun 2023.

Builds on

27 of 92 references.

References · 27

  1. 2018A Tutorial on Bayesian Optimizationcited by 734
  2. 2021Therapeutics Data Commons: Machine Learning Datasets and Tasks for Drug Discovery and Developmentcited by 258
  3. 2014Predictive Entropy Search for Efficient Global Optimization of Black-box Functionscited by 201
  4. 2020Fast Differentiable Sorting and Rankingcited by 196
  5. 2020Differentiable Expected Hypervolume Improvement for Parallel Multi-Objective Bayesian Optimizationcited by 176
  6. 2021Parallel Bayesian Optimization of Multiple Noisy Objectives with Expected Hypervolume Improvementcited by 115
  7. 2018Maximizing acquisition functions for Bayesian optimizationcited by 113
  8. 2019Differentiable Ranks and Sorting using Optimal Transportcited by 113
  9. 2018A Flexible Framework for Multi-Objective Bayesian Optimization using Random Scalarizationscited by 98
  10. 2015Predictive Entropy Search for Multi-objective Bayesian Optimizationcited by 88
  11. 2020Scalable Constrained Bayesian Optimizationcited by 84
  12. 2020Max-value Entropy Search for Multi-Objective Bayesian Optimization with Constraintscited by 81
15 more
  1. 2022Joint Entropy Search for Maximally-Informed Bayesian Optimizationcited by 55
  2. 2015A General Framework for Constrained Bayesian Optimization using Information-based Searchcited by 50
  3. 2022Joint Entropy Search for Multi-objective Bayesian Optimizationcited by 45
  4. 2022Robust Multi-Objective Bayesian Optimization Under Input Noisecited by 36
  5. 2022Bayesian Optimization over Discrete and Mixed Spaces via Probabilistic Reparameterizationcited by 35
  6. 2015Parallel Predictive Entropy Search for Batch Global Optimization of Expensive Objective Functionscited by 31
  7. 2019Efficient Computation of Expected Hypervolume Improvement Using Box Decomposition Algorithmscited by 24
  8. 2015Evading the curse of dimensionality in nonparametric density estimation with simplified vine copulascited by 18
  9. 2017Nonparametric estimation of simplified vine copula models: comparison of methodscited by 13
  10. 2019The Kalai-Smorodinski solution for many-objective Bayesian optimizationcited by 13
  11. 2014Probit transformation for nonparametric kernel estimation of the copula densitycited by 9
  12. 2022PropertyDAG: Multi-objective Bayesian optimization of partially ordered, mixed-variable properties for biological sequence designcited by 8
  13. 2019Ordinal Bayesian Optimisationcited by 7
  14. 2022A Pareto-optimal compositional energy-based model for sampling and optimization of protein sequencescited by 7
  15. 2023Retrospective Uncertainties for Deep Models using Vine Copulascited by 7

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Citing papers per year: 2024: 4; 2025: 6; 2026: 4.

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  1. 2024ParetoFlow: Guided Flows in Multi-Objective Optimizationcited by 17
  2. 2024Semiparametric conformal predictioncited by 13
  3. 2025TR2-D2: Tree Search Guided Trajectory-Aware Fine-Tuning for Discrete Diffusioncited by 13
  4. 2025Diffusion and Flow-based Copulas: Forgetting and Remembering Dependenciescited by 7
  5. 2024Constrained Multi-objective Bayesian Optimization through Optimistic Constraints Estimationcited by 6
  6. 2025Vine Copulas as Differentiable Computational Graphscited by 2
  7. 2026Do We Really Need to Approach the Entire Pareto Front in Many-Objective Bayesian Optimisation?cited by 2
  8. 2025COPA: Comparing the incomparable in multi-objective model evaluationcited by 1
  9. 2025Learning Design-Score Manifold to Guide Diffusion Models for Offline Optimizationcited by 1
  10. 2025Throwing Vines at the Wall: Structure Learning via Random Searchcited by 1
  11. 2026Auto-Configured Networks for Multi-Scale Multi-Output Time-Series Forecastingcited by 1
  12. 2024Training Greedy Policy for Proposal Batch Selection in Expensive Multi-Objective Combinatorial Optimizationcited by 0
2 more
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  2. 2026Converge Then Diversify: Decoupling Convergence and Diversity in Multi-Objective Bayesian Optimisationcited by 0