  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.
