Bayesian optimization with approximate set kernels

We propose a practical Bayesian optimization method over sets, to minimize black-box function that takes set as single input. Because inputs are permutation-invariant, traditional Gaussian process-based strategies which assume vector can fall short. To address this, we develop with kernel is used build surrogate functions. This accumulates similarity elements enforce permutation-invariance, but this comes at greater computational cost. reduce burden, two key components: (i) more efficient approximate still positive-definite and an unbiased estimator of the true upper-bounded variance in terms number subsamples, (ii) constrained acquisition uses symmetry feasible region defines Finally, present several numerical experiments demonstrate our outperforms other methods.