论文标题
无需重新格雷算法多任务贝叶斯优化
No-regret Algorithms for Multi-task Bayesian Optimization
论文作者
论文摘要
我们考虑非参数贝叶斯优化（BO）设置中未知矢量值函数的多目标优化（MOO），目的是在目标的帕雷托方面学习要点。大多数现有的BO算法并没有模仿以下事实：多个目标或等效地，任务可以共享相似之处，甚至少数确实缺乏严格，有限的遗憾的人也可以确保捕获明确的任务间结构。在这项工作中，我们通过使用多任务内核对任务间依赖关系进行建模，并基于目标的随机标量来建立两种新颖的BO算法。我们的算法采用矢量价值的内核回归作为垫脚石，属于算法的上置信度界限。在平稳性的假设下，未知的矢量值函数是与多任务内核相关的再现内核希尔伯特空间的一个元素，我们为明确捕获任务之间相似之处的算法而得出了最坏的案例后悔界限。我们在数字上基于合成和现实生活中的MOO问题基准了我们的算法，并显示了使用多任务内核提供的优势。
We consider multi-objective optimization (MOO) of an unknown vector-valued function in the non-parametric Bayesian optimization (BO) setting, with the aim being to learn points on the Pareto front of the objectives. Most existing BO algorithms do not model the fact that the multiple objectives, or equivalently, tasks can share similarities, and even the few that do lack rigorous, finite-time regret guarantees that capture explicitly inter-task structure. In this work, we address this problem by modelling inter-task dependencies using a multi-task kernel and develop two novel BO algorithms based on random scalarizations of the objectives. Our algorithms employ vector-valued kernel regression as a stepping stone and belong to the upper confidence bound class of algorithms. Under a smoothness assumption that the unknown vector-valued function is an element of the reproducing kernel Hilbert space associated with the multi-task kernel, we derive worst-case regret bounds for our algorithms that explicitly capture the similarities between tasks. We numerically benchmark our algorithms on both synthetic and real-life MOO problems, and show the advantages offered by learning with multi-task kernels.
