Scalable Bayesian Optimization via Focalized Sparse Gaussian Processes

TL;DR

This paper introduces FocalBO, a scalable Bayesian optimization method using focalized sparse Gaussian processes that efficiently allocates modeling capacity to relevant regions, enabling high-dimensional optimization with large datasets.

Contribution

The paper proposes a novel focalized Gaussian process model and a hierarchical optimization algorithm, FocalBO, to improve scalability and local accuracy in high-dimensional Bayesian optimization.

Findings

Achieves state-of-the-art results in robot morphology design.

Effectively controls a 585-dimensional musculoskeletal system.

Leverages large offline and online datasets efficiently.

Abstract

Bayesian optimization is an effective technique for black-box optimization, but its applicability is typically limited to low-dimensional and small-budget problems due to the cubic complexity of computing the Gaussian process (GP) surrogate. While various approximate GP models have been employed to scale Bayesian optimization to larger sample sizes, most suffer from overly-smooth estimation and focus primarily on problems that allow for large online samples. In this work, we argue that Bayesian optimization algorithms with sparse GPs can more efficiently allocate their representational power to relevant regions of the search space. To achieve this, we propose focalized GP, which leverages a novel variational loss function to achieve stronger local prediction, as well as FocalBO, which hierarchically optimizes the focalized GP acquisition function over progressively smaller search spaces. Experimental results demonstrate that FocalBO can efficiently leverage large amounts of offline and online data to achieve state-of-the-art performance on robot morphology design and to control a 585-dimensional musculoskeletal system.