High-Dimensional Bayesian Optimization via Tree-Structured Additive Models

TL;DR

This paper introduces a tree-structured additive model approach to high-dimensional Bayesian Optimization, reducing computational complexity and improving efficiency in continuous domains.

Contribution

It proposes a hybrid graph learning algorithm and a zooming-based optimization method for scalable, sample-efficient high-dimensional Bayesian Optimization.

Findings

Effective in synthetic function experiments

Demonstrates improved efficiency on real-world datasets

Reduces computational resources compared to traditional methods

Abstract

Bayesian Optimization (BO) has shown significant success in tackling expensive low-dimensional black-box optimization problems. Many optimization problems of interest are high-dimensional, and scaling BO to such settings remains an important challenge. In this paper, we consider generalized additive models in which low-dimensional functions with overlapping subsets of variables are composed to model a high-dimensional target function. Our goal is to lower the computational resources required and facilitate faster model learning by reducing the model complexity while retaining the sample-efficiency of existing methods. Specifically, we constrain the underlying dependency graphs to tree structures in order to facilitate both the structure learning and optimization of the acquisition function. For the former, we propose a hybrid graph learning algorithm based on Gibbs sampling and mutation. In addition, we propose a novel zooming-based algorithm that permits generalized additive models to be employed more efficiently in the case of continuous domains. We demonstrate and discuss the efficacy of our approach via a range of experiments on synthetic functions and real-world datasets.