Topological Bayesian Optimization with Persistence Diagrams

TL;DR

This paper introduces topological Bayesian optimization that leverages persistent homology to efficiently optimize structured data, such as material and neural network structures, by measuring topological similarities.

Contribution

It proposes a novel Bayesian optimization method that incorporates topological information via persistence diagrams, enabling optimization over complex structured data.

Findings

Outperforms random search in structure optimization tasks.

Effective in handling multiple types of topological information.

Improves search efficiency over existing graph Bayesian optimization.

Abstract

Finding an optimal parameter of a black-box function is important for searching stable material structures and finding optimal neural network structures, and Bayesian optimization algorithms are widely used for the purpose. However, most of existing Bayesian optimization algorithms can only handle vector data and cannot handle complex structured data. In this paper, we propose the topological Bayesian optimization, which can efficiently find an optimal solution from structured data using \emph{topological information}. More specifically, in order to apply Bayesian optimization to structured data, we extract useful topological information from a structure and measure the proper similarity between structures. To this end, we utilize persistent homology, which is a topological data analysis method that was recently applied in machine learning. Moreover, we propose the Bayesian optimization algorithm that can handle multiple types of topological information by using a linear combination of kernels for persistence diagrams. Through experiments, we show that topological information extracted by persistent homology contributes to a more efficient search for optimal structures compared to the random search baseline and the graph Bayesian optimization algorithm.