Bayesian Optimization over Permutation Spaces

• URL: http://arxiv.org/abs/2112.01049v1
• Date: Thu, 2 Dec 2021 08:20:50 GMT
• Title: Bayesian Optimization over Permutation Spaces
• Authors: Aryan Deshwal, Syrine Belakaria, Janardhan Rao Doppa, Dae Hyun Kim
• Abstract summary: We propose and evaluate two algorithms for BO over Permutation Spaces (BOPS) 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 spaces.
• Score: 30.650753803587794
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 based on Thompson sampling 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 expected improvement 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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