论文标题
超越网格：自适应离散化的多目标贝叶斯优化
Beyond Grids: Multi-objective Bayesian Optimization With Adaptive Discretization
论文作者
论文摘要
我们考虑了优化矢量价值的目标函数$ \ boldsymbol {f} $从高斯过程（GP）采样的问题，其索引集是一个行为良好的，紧凑的度量空间$（{\ cal x}，d）$的设计。我们假设$ \ boldsymbol {f} $事先未知，并且在design $ x $上评估$ \ boldsymbol {f} $会导致对$ \ boldsymbol {f}（x）$的嘈杂观察。由于当$ {\ cal x} $的基数很大时，通过详尽的搜索确定帕累托的最佳设计是不可行的，因此我们提出了一种称为Adaptive $ \boldsymbolε$ -PAL的算法，利用了GP-Samplyed功能的平稳性和$（\ cal x} $ delce fack fack）。从本质上讲，自适应$ \boldsymbolε$ -PAL采用基于树的自适应离散技术来识别$ \boldsymbolε$ -Carcurate Pareto的设计，以尽可能少的评估进行。我们在$ \boldsymbolε$ -Cpurate Pareto设置识别的样本复杂性上同时提供信息类型和度量尺寸型界限。我们还通过实验表明，我们的算法表现优于其他帕累托集识别方法。
We consider the problem of optimizing a vector-valued objective function $\boldsymbol{f}$ sampled from a Gaussian Process (GP) whose index set is a well-behaved, compact metric space $({\cal X},d)$ of designs. We assume that $\boldsymbol{f}$ is not known beforehand and that evaluating $\boldsymbol{f}$ at design $x$ results in a noisy observation of $\boldsymbol{f}(x)$. Since identifying the Pareto optimal designs via exhaustive search is infeasible when the cardinality of ${\cal X}$ is large, we propose an algorithm, called Adaptive $\boldsymbolε$-PAL, that exploits the smoothness of the GP-sampled function and the structure of $({\cal X},d)$ to learn fast. In essence, Adaptive $\boldsymbolε$-PAL employs a tree-based adaptive discretization technique to identify an $\boldsymbolε$-accurate Pareto set of designs in as few evaluations as possible. We provide both information-type and metric dimension-type bounds on the sample complexity of $\boldsymbolε$-accurate Pareto set identification. We also experimentally show that our algorithm outperforms other Pareto set identification methods.
