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Title: Bayesian Optimization over Permutation Spaces
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.  more » « less
Award ID(s):
2030159
PAR ID:
10351762
Author(s) / Creator(s):
; ; ;
Date Published:
Journal Name:
Proceedings of the AAAI Conference on Artificial Intelligence
Volume:
36
Issue:
6
ISSN:
2159-5399
Page Range / eLocation ID:
6515 to 6523
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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