# Expected Diverse Utility (EDU): Diverse Bayesian Optimization of Expensive Computer Simulators

arXiv: https://arxiv.org/abs/2410.01196 · HTML: https://mlsanity.com/paper/2410.01196/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 71 references that are in the map.
- First posted on arXiv 2 Oct 2024.

## Builds on (most cited first, 17 of 17)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Deep Learning in Neural Networks: An Overview](https://mlsanity.com/paper/1404.7828/) (2014)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Unexpected Improvements to Expected Improvement for Bayesian Optimization](https://mlsanity.com/paper/2310.20708/) (2023)
- [Batched Large-scale Bayesian Optimization in High-dimensional Spaces](https://mlsanity.com/paper/1706.01445/) (2017)
- [The Parallel Knowledge Gradient Method for Batch Bayesian Optimization](https://mlsanity.com/paper/1606.04414/) (2016)
- [Adversarially Robust Optimization with Gaussian Processes](https://mlsanity.com/paper/1810.10775/) (2018)
- [Discovering Many Diverse Solutions with Bayesian Optimization](https://mlsanity.com/paper/2210.10953/) (2022)
- [Bayesian Optimization for Synthetic Gene Design](https://mlsanity.com/paper/1505.01627/) (2015)
- [A hierarchical expected improvement method for Bayesian optimization](https://mlsanity.com/paper/1911.07285/) (2019)
- [Triangulation candidates for Bayesian optimization](https://mlsanity.com/paper/2112.07457/) (2021)
- [Function-on-function kriging, with applications to 3D printing of aortic tissues](https://mlsanity.com/paper/1910.01754/) (2019)
- [Contour Location for Reliability in Airfoil Simulation Experiments using Deep Gaussian Processes](https://mlsanity.com/paper/2308.04420/) (2023)
- [Additive Multi-Index Gaussian process modeling, with application to multi-physics surrogate modeling of the quark-gluon plasma](https://mlsanity.com/paper/2306.07299/) (2023)
- [Robust expected improvement for Bayesian optimization](https://mlsanity.com/paper/2302.08612/) (2023)
- [Targeted Variance Reduction: Robust Bayesian Optimization of Black-Box Simulators with Noise Parameters](https://mlsanity.com/paper/2403.03816/) (2024)

## Built on by (most cited first, 3 of 3)

- [Efficient optimization of expensive black-box simulators via marginal means, with application to neutrino detector design](https://mlsanity.com/paper/2508.01834/) (2025)
- [Neural Low-Discrepancy Sequences](https://mlsanity.com/paper/2510.03745/) (2025)
- [Isotonic surrogate modeling for computer experiments with many input variables](https://mlsanity.com/paper/2609.35354/) (2026)

## Abstract (arXiv)

The optimization of expensive black-box simulators arises in a myriad of modern scientific and engineering applications. Bayesian optimization provides an appealing solution, by leveraging a fitted surrogate model to guide the selection of subsequent simulator evaluations. In practice, however, the objective is often not to obtain a single good solution, but rather a ``basket'' of good solutions from which users can choose for downstream decision-making. This need arises in our motivating application for real-time control of internal combustion engines for flight propulsion, where a diverse set of control strategies is essential for stable flight control. There has been little work on this front for Bayesian optimization. We thus propose a new Expected Diverse Utility (EDU) method that searches for diverse ``ε-optimal'' solutions: locally-optimal solutions within a tolerance level ε > 0 from a global optimum. We show that EDU yields a closed-form acquisition function under a Gaussian process surrogate model, which facilitates efficient sequential queries via automatic differentiation. This closed form further reveals a novel exploration-exploitation-diversity trade-off, which incorporates the desired diversity property within the well-known exploration-exploitation trade-off. We demonstrate the improvement of EDU over existing methods in a suite of numerical experiments, then explore the EDU in two applications on rover trajectory optimization and engine control for flight propulsion.