mlsanityData to 7 Oct 2026

Unexpected Improvements to Expected Improvement for Bayesian Optimization

arXiv 2310.20708 ↗First posted 31 Oct 2023cs.LG cs.NA math.NAcited by 144

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Abstract (arXiv)

Expected Improvement (EI) is arguably the most popular acquisition function in Bayesian optimization and has found countless successful applications, but its performance is often exceeded by that of more recent methods. Notably, EI and its variants, including for the parallel and multi-objective settings, are challenging to optimize because their acquisition values vanish numerically in many regions. This difficulty generally increases as the number of observations, dimensionality of the search space, or the number of constraints grow, resulting in performance that is inconsistent across the literature and most often sub-optimal. Herein, we propose LogEI, a new family of acquisition functions whose members either have identical or approximately equal optima as their canonical counterparts, but are substantially easier to optimize numerically. We demonstrate that numerical pathologies manifest themselves in "classic" analytic EI, Expected Hypervolume Improvement (EHVI), as well as their constrained, noisy, and parallel variants, and propose corresponding reformulations that remedy these pathologies. Our empirical results show that members of the LogEI family of acquisition functions substantially improve on the optimization performance of their canonical counterparts and surprisingly, are on par with or exceed the performance of recent state-of-the-art acquisition functions, highlighting the understated role of numerical optimization in the literature.

Key facts. Cited by 144 papers in the map (data through 7 Oct 2026). Builds on 42 of its 78 references that are in the map. First posted on arXiv 31 Oct 2023.

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42 of 78 references.

References · 42

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  1. 2019Combinatorial Bayesian Optimization using the Graph Cartesian Productcited by 78
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  25. 2021Triangulation candidates for Bayesian optimizationcited by 11
  26. 2023Trieste: Efficiently Exploring The Depths of Black-box Functions with TensorFlowcited by 11
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Citing papers per year: 2023: 1; 2024: 31; 2025: 50; 2026: 62.

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  5. 2025Reasoning BO: Enhancing Bayesian Optimization with Long-Context Reasoning Power of LLMscited by 8
  6. 2024Robust Gaussian Processes via Relevance Pursuitcited by 7
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  11. 2025NeST-BO: Fast Local Bayesian Optimization via Newton-Step Targeting of Gradient and Hessian Informationcited by 6
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  16. 2024Model Fusion through Bayesian Optimization in Language Model Fine-Tuningcited by 5
  17. 2025BONSAI: Structure-exploiting robust Bayesian optimization for networked black-box systems under uncertaintycited by 5
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  19. 2026Agentic Bayesian Optimization through Surrogate-Augmented Autoresearchcited by 5
  20. 2024Accelerating Look-ahead in Bayesian Optimization: Multilevel Monte Carlo is All you Needcited by 4
  21. 2024TS-RSR: A provably efficient approach for batch Bayesian Optimizationcited by 4
  22. 2024CAGES: Cost-Aware Gradient Entropy Search for Efficient Local Multi-Fidelity Bayesian Optimizationcited by 4
  23. 2025Posterior Inference in Latent Space for Scalable Constrained Black-box Optimizationcited by 4
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  25. 2025Cooperative Design Optimization through Natural Language Interactioncited by 4
  26. 2025A Unified Framework for Entropy Search and Expected Improvement in Bayesian Optimizationcited by 3
  27. 2025Pareto-frontier Entropy Search with Variational Lower Bound Maximizationcited by 3
  28. 2025High Dimensional Bayesian Optimization using Lasso Variable Selectioncited by 3
  29. 2025Regret Analysis of Posterior Sampling-Based Expected Improvement for Bayesian Optimizationcited by 3
  30. 2025Sampling from Gaussian Processes: A Tutorial and Applications in Global Sensitivity Analysis and Optimizationcited by 3
  31. 2024On the development of a practical Bayesian optimisation algorithm for expensive experiments and simulations with changing environmental conditionscited by 2
  32. 2024Parameter Identification for Electrochemical Models of Lithium-Ion Batteries Using Bayesian Optimizationcited by 2
  33. 2024BEACON: A Bayesian Optimization Inspired Strategy for Efficient Novelty Searchcited by 2
  34. 2024Expected Diverse Utility (EDU): Diverse Bayesian Optimization of Expensive Computer Simulatorscited by 2
  35. 2024Batched Bayesian optimization by maximizing the probability of including the optimumcited by 2
  36. 2024Derivation of Closed Form of Expected Improvement for Gaussian Process Trained on Log-Transformed Objectivecited by 2
  37. 2025Towards Scalable Bayesian Optimization via Gradient-Informed Bayesian Neural Networkscited by 2
  38. 2025Learning Explainable Dense Reward Shapes via Bayesian Optimizationcited by 2

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