mlsanityData to 14 Oct 2026

Joint Entropy Search for Multi-objective Bayesian Optimization

arXiv 2210.02905 ↗First posted 6 Oct 2022cs.LG math.OC stat.MLcited by 45

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Abstract (arXiv)

Many real-world problems can be phrased as a multi-objective optimization problem, where the goal is to identify the best set of compromises between the competing objectives. Multi-objective Bayesian optimization (BO) is a sample efficient strategy that can be deployed to solve these vector-valued optimization problems where access is limited to a number of noisy objective function evaluations. In this paper, we propose a novel information-theoretic acquisition function for BO called Joint Entropy Search (JES), which considers the joint information gain for the optimal set of inputs and outputs. We present several analytical approximations to the JES acquisition function and also introduce an extension to the batch setting. We showcase the effectiveness of this new approach on a range of synthetic and real-world problems in terms of the hypervolume and its weighted variants.

Key facts. Cited by 45 papers in the map (data through 14 Oct 2026). Builds on 55 of its 117 references that are in the map. First posted on arXiv 6 Oct 2022.

Builds on

55 of 117 references.

References · 55

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38 more
  1. 2017Multi-fidelity Bayesian Optimisation with Continuous Approximationscited by 121
  2. 2021Parallel Bayesian Optimization of Multiple Noisy Objectives with Expected Hypervolume Improvementcited by 118
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  5. 2018A Flexible Framework for Multi-Objective Bayesian Optimization using Random Scalarizationscited by 99
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  7. 2015Predictive Entropy Search for Multi-objective Bayesian Optimizationcited by 88
  8. 2021Multi-Objective Bayesian Optimization over High-Dimensional Search Spacescited by 87
  9. 2020Max-value Entropy Search for Multi-Objective Bayesian Optimization with Constraintscited by 81
  10. 2018Stagewise Safe Bayesian Optimization with Gaussian Processescited by 79
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  14. 2020Random Hypervolume Scalarizations for Provable Multi-Objective Black Box Optimizationcited by 60
  15. 2019Multi-objective Bayesian Optimization using Pareto-frontier Entropycited by 57
  16. 2019Bayesian Optimisation over Multiple Continuous and Categorical Inputscited by 56
  17. 2022Joint Entropy Search for Maximally-Informed Bayesian Optimizationcited by 55
  18. 2018A General Framework for Multi-fidelity Bayesian Optimization with Gaussian Processescited by 52
  19. 2015Predictive Entropy Search for Bayesian Optimization with Unknown Constraintscited by 51
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  21. 2013Parallel Gaussian Process Optimization with Upper Confidence Bound and Pure Explorationcited by 50
  22. 2015A General Framework for Constrained Bayesian Optimization using Information-based Searchcited by 50
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  27. 2021Bayesian Algorithm Execution: Estimating Computable Properties of Black-box Functions Using Mutual Informationcited by 33
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  29. 2019Bayesian Optimization for Categorical and Category-Specific Continuous Inputscited by 28
  30. 2016Predictive Entropy Search for Multi-objective Bayesian Optimization with Constraintscited by 27
  31. 2019Efficient Computation of Expected Hypervolume Improvement Using Box Decomposition Algorithmscited by 24
  32. 2021Sequential- and Parallel- Constrained Max-value Entropy Search via Information Lower Boundcited by 23
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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 1; 2023: 11; 2024: 8; 2025: 13; 2026: 12.

45 papers.

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  2. 2023Self-Correcting Bayesian Optimization through Bayesian Active Learningcited by 22
  3. 2023A General Framework for User-Guided Bayesian Optimizationcited by 22
  4. 2025Gradient-Based Multi-Objective Deep Learning: Algorithms, Theories, Applications, and Beyondcited by 18
  5. 2022Combining Multi-Fidelity Modelling and Asynchronous Batch Bayesian Optimizationcited by 16
  6. 2023BOtied: Multi-objective Bayesian optimization with tied multivariate rankscited by 15
  7. 2023qPOTS: Efficient batch multiobjective Bayesian optimization via Pareto optimal Thompson samplingcited by 11
  8. 2025BOFormer: Learning to Solve Multi-Objective Bayesian Optimization via Non-Markovian RLcited by 10
  9. 2025Exploring Exploration in Bayesian Optimizationcited by 9
  10. 2026Adaptive Acquisition Selection for Bayesian Optimization with Large Language Modelscited by 9
  11. 2023Gaussian Max-Value Entropy Search for Multi-Agent Bayesian Optimizationcited by 7
  12. 2024Transition Constrained Bayesian Optimization via Markov Decision Processescited by 7
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  1. 2023Knowledge Gradient for Multi-Objective Bayesian Optimization with Decoupled Evaluationscited by 5
  2. 2024Optimizing Posterior Samples for Bayesian Optimization via Rootfindingcited by 5
  3. 2025Regret Analysis of Posterior Sampling-Based Expected Improvement for Bayesian Optimizationcited by 4
  4. 2023Multi-objective optimisation via the R2 utilitiescited by 3
  5. 2023Bayesian Optimisation Against Climate Change: Applications and Benchmarkscited by 3
  6. 2023Multi-Objective Optimization via Wasserstein-Fisher-Rao Gradient Flowcited by 3
  7. 2025A Unified Framework for Entropy Search and Expected Improvement in Bayesian Optimizationcited by 3
  8. 2025Pareto-frontier Entropy Search with Variational Lower Bound Maximizationcited by 3
  9. 2025MOBO-OSD: Batch Multi-Objective Bayesian Optimization via Orthogonal Search Directionscited by 3
  10. 2023Practical Path-based Bayesian Optimizationcited by 2
  11. 2025Information-theoretic Bayesian Optimization: Survey and Tutorialcited by 2
  12. 2025FoMEMO: Towards Foundation Models for Expensive Multi-objective Optimizationcited by 2
  13. 2025Informed Initialization for Bayesian Optimization and Active Learningcited by 2
  14. 2026Do We Really Need to Approach the Entire Pareto Front in Many-Objective Bayesian Optimisation?cited by 2
  15. 2026α-PFN: Fast Entropy Search via In-Context Learningcited by 2
  16. 2024Variational Entropy Search for Adjusting Expected Improvementcited by 1
  17. 2024Scalarisation-based risk concepts for robust multi-objective optimisationcited by 1
  18. 2024Alpha Entropy Search for New Information-based Bayesian Optimizationcited by 1
  19. 2025Amortized Multi-Objective Optimization Across Tasks with Generative Solution Modelingcited by 1
  20. 2025Local Entropy Search over Descent Sequences for Bayesian Optimizationcited by 1
  21. 2026BoLT: A Benchmark to Democratize Black-box Optimization Research for Expensive LLM Taskscited by 1
  22. 2026Enhancing Bayesian Optimization and Active Learning Through Kernel Diversitycited by 1
  23. 2024Training Greedy Policy for Proposal Batch Selection in Expensive Multi-Objective Combinatorial Optimizationcited by 0
  24. 2024Vector Optimization with Gaussian Process Banditscited by 0
  25. 2024Non-Myopic Multi-Objective Bayesian Optimizationcited by 0
  26. 2025Information-Theoretic Bayesian Optimization for Bilevel Optimization Problemscited by 0
  27. 2026Combinatorial Bandit Bayesian Optimization for Tensor Outputscited by 0
  28. 2026Multi-Objective Bayesian Optimization via Adaptive varepsilon-Constraints Decompositioncited by 0
  29. 2026Towards Regret Guarantees for One-Step Lookahead Bayesian Optimizationcited by 0
  30. 2026Converge Then Diversify: Decoupling Convergence and Diversity in Multi-Objective Bayesian Optimisationcited by 0
  31. 2026Simple Extensions of Single-Objective Acquisition Functions and Hedge Strategies for Multi-Objective Bayesian Optimizationcited by 0
  32. 2026Adapting Nonstationary Multi-output Gaussian Processes to Bayesian Optimizationcited by 0
  33. 2026Learning What to Evaluate: Correlation-Aware Decoupling for Multiobjective Bayesian Optimizationcited by 0