CMX Lunch Seminar
We consider the issue of modeling and optimizing set functions, with a main focus on kernel methods for expensive objective functions taking finite sets as inputs. Based on recent developments on embeddings of probability distributions in Reproducing Kernel Hilbert Spaces, we explore adaptations of Gaussian Process modeling and Bayesian Optimization to the framework of interest. In particular, combining RKHS embeddings and positive definite kernels on Hilbert spaces delivers a promising class of kernels, as illustrated in particular on two test cases from mechanical engineering and contaminant source localization, respectively. Based on several collaborations and notably on the paper "Kernels over sets of finite sets using RKHS embeddings, with application to Bayesian (combinatorial) optimization" with Poompol Buathong and Tipaluck Krityakierne (AISTATS 2020).