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In this work we propose a batch Bayesian optimization method forcombinatorial problems on permutations, which is well suited forexpensive-to-evaluate objectives. We first introduce LAW, an efficient batchacquisition method based on determinantal point processes using the acquisitionweighted kernel. Relying on multiple parallel evaluations, LAW enablesaccelerated search on combinatorial spaces. We then apply the framework topermutation problems, which have so far received little attention in theBayesian Optimization literature, despite their practical importance. We callthis method LAW2ORDER. On the theoretical front, we prove that LAW2ORDER hasvanishing simple regret by showing that the batch cumulative regret issublinear. Empirically, we assess the method on several standard combinatorialproblems involving permutations such as quadratic assignment, flowshopscheduling and the traveling salesman, as well as on a structure learning task.

Batch Bayesian Optimization on Permutations using the Acquisition Weighted Kernel