Diverse Expected Improvement (DEI): Diverse Bayesian Optimization of Expensive Computer Simulators
<|reference_start|>Diverse Expected Improvement (DEI): Diverse Bayesian Optimization of Expensive Computer Simulators: 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 Diverse Expected Improvement (DEI) method that searches for diverse ''$\epsilon$-optimal'' solutions: locally-optimal solutions within a tolerance level $\epsilon > 0$ from a global optimum. We show that DEI 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 DEI over existing methods in a suite of numerical experiments, then explore the DEI in two applications on rover trajectory optimization and engine control for flight propulsion.<|reference_end|>
@article{miller2024diverse,
    title={Diverse Expected Improvement (DEI): Diverse Bayesian Optimization of
  Expensive Computer Simulators},
    author={John Joshua Miller, Simon Mak, Benny Sun, Sai Ranjeet Narayanan, Suo
  Yang, Zongxuan Sun, Kenneth S. Kim, Chol-Bum Mike Kweon},
    journal={arXiv preprint arXiv:2410.01196},
    year={2024},
    archivePrefix={arXiv},
    eprint={2410.01196},
    primaryClass={stat.AP cs.LG stat.ML}
}