Optimizing expensive to evaluate black-box functions over an input space consisting of all permutations of d objects is an important problem with many real-world applications. For example, placement of functional blocks in hardware design to optimize performance via simulations. The overall goal is to minimize the number of function evaluations to find high-performing permutations. The key challenge in solving this problem using the Bayesian optimization (BO) framework is to trade-off the complexity of statistical model and tractability of acquisition function optimization. In this paper, we propose and evaluate two algorithms for BO over Permutation Spaces (BOPS). First, BOPS-T employs Gaussian process (GP) surrogate model with Kendall kernels and a Tractable acquisition function optimization approach to select the sequence of permutations for evaluation. Second, BOPS-H employs GP surrogate model with Mallow kernels and a Heuristic search approach to optimize the acquisition function. We theoretically analyze the performance of BOPS-T to show that their regret grows sub-linearly. Our experiments on multiple synthetic and real-world benchmarks show that both BOPS-T and BOPS-H perform better than the state-of-the-art BO algorithm for combinatorial spaces. To drive future research on this important problem, we make new resources and real-world benchmarks available to the community.
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Benchmarking the performance of Bayesian optimization across multiple experimental materials science domains
Bayesian optimization (BO) has been leveraged for guiding autonomous and high-throughput experiments in materials science. However, few have evaluated the efficiency of BO across a broad range of experimental materials domains. In this work, we quantify the performance of BO with a collection of surrogate model and acquisition function pairs across five diverse experimental materials systems. By defining acceleration and enhancement metrics for materials optimization objectives, we find that surrogate models such as Gaussian Process (GP) with anisotropic kernels and Random Forest (RF) have comparable performance in BO, and both outperform the commonly used GP with isotropic kernels. GP with anisotropic kernels has demonstrated the most robustness, yet RF is a close alternative and warrants more consideration because it is free from distribution assumptions, has smaller time complexity, and requires less effort in initial hyperparameter selection. We also raise awareness about the benefits of using GP with anisotropic kernels in future materials optimization campaigns.
more » « less- NSF-PAR ID:
- 10307656
- Publisher / Repository:
- Nature Publishing Group
- Date Published:
- Journal Name:
- npj Computational Materials
- Volume:
- 7
- Issue:
- 1
- ISSN:
- 2057-3960
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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