In this work we propose a batch Bayesian optimization method for combinatorial problems on permutations, which is well suited for expensive-to-evaluate objectives. We first introduce LAW, an efficient batch acquisition method based on determinantal point processes using the acquisition weighted kernel. Relying on multiple parallel evaluations, LAW enables accelerated search on combinatorial spaces. We then apply the framework to permutation problems, which have so far received little attention in the Bayesian Optimization literature, despite their practical importance. We call this method LAW2ORDER. On the theoretical front, we prove that LAW2ORDER has vanishing simple regret by showing that the batch cumulative regret is sublinear. Empirically, we assess the method on several standard combinatorial problems involving permutations such as quadratic assignment, flowshop scheduling and the traveling salesman, as well as on a structure learning task.

翻译：在这项工作中,我们提出了一组巴伊西亚混合问题优化方法,该方法非常适合昂贵的估算目标。我们首先引入了Law,这是一种基于使用获取加权内核的决定性点过程的高效批量获取方法。依靠多重平行评估,Law能够加速搜索组合空间。然后我们运用这一框架处理混合问题,尽管这些问题在Bayesian Oppimization文献中具有实际重要性,但至今没有受到多少关注。我们称之为Law2ORDER。在理论方面,我们证明Law2ORDER通过显示批量累积遗憾是次线性的,简单地消除了遗憾。我们很生动地评估了涉及四面形分配、流动车间时间安排和旅行销售人员等若干标准组合问题的方法,以及结构学习任务。