Molding into graph

Abstract

Solving black-box optimization is critical in the sense that most of the real-world problems do not provide explicit problem formulation. Despite the success of Bayesian optimization for such problems, most of the works have been made under the assumption of continuous input domains. However, a number of real- world applications also involve ordinal or nominal variables in their search spaces. In this work, we focused on optimizing such mixed search spaces where different types of variables coexist. We introduce a novel perspective where we mold the data into an appropriate graph structure (i.e. each dimension represents a distinct node) where its connectivity would take its role as a kernel. In detail, we adopt latent space optimization framework with graph neural network as an encoder so that interactions between different variables can be naturally aggregated by the message passing scheme. We first empirically validate our approach and propose a new framework of jointly searching appropriate graph structure (kernel) and optimizing downstream task. Experimental results show that our method demonstrates high efficiency comparing to state-of-the-art algorithms on various tasks regarding computation time.