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- Title
Bayesian optimization with approximate set kernels.
- Authors
Kim, Jungtaek; McCourt, Michael; You, Tackgeun; Kim, Saehoon; Choi, Seungjin
- Abstract
We propose a practical Bayesian optimization method over sets, to minimize a black-box function that takes a set as a single input. Because set inputs are permutation-invariant, traditional Gaussian process-based Bayesian optimization strategies which assume vector inputs can fall short. To address this, we develop a Bayesian optimization method with set kernel that is used to build surrogate functions. This kernel accumulates similarity over set elements to enforce permutation-invariance, but this comes at a greater computational cost. To reduce this burden, we propose two key components: (i) a more efficient approximate set kernel which is still positive-definite and is an unbiased estimator of the true set kernel with upper-bounded variance in terms of the number of subsamples, (ii) a constrained acquisition function optimization over sets, which uses symmetry of the feasible region that defines a set input. Finally, we present several numerical experiments which demonstrate that our method outperforms other methods.
- Subjects
GLOBAL optimization; SYMMETRY; KERNEL functions
- Publication
Machine Learning, 2021, Vol 110, Issue 5, p857
- ISSN
0885-6125
- Publication type
Article
- DOI
10.1007/s10994-021-05949-0