Re-Examining Linear Embeddings for High-Dimensional Bayesian Optimization

TL;DR

This paper critically examines linear embeddings in high-dimensional Bayesian optimization, identifying issues and demonstrating that addressing these improves performance on complex problems like robot gait learning.

Contribution

It highlights misconceptions in existing linear embedding methods for BO and empirically shows how proper adjustments enhance optimization effectiveness.

Findings

Addressing key issues improves BO performance

Linear embeddings can be effective with correct design choices

Empirical results on robot gait learning demonstrate improvements

Abstract

Bayesian optimization (BO) is a popular approach to optimize expensive-to-evaluate black-box functions. A significant challenge in BO is to scale to high-dimensional parameter spaces while retaining sample efficiency. A solution considered in existing literature is to embed the high-dimensional space in a lower-dimensional manifold, often via a random linear embedding. In this paper, we identify several crucial issues and misconceptions about the use of linear embeddings for BO. We study the properties of linear embeddings from the literature and show that some of the design choices in current approaches adversely impact their performance. We show empirically that properly addressing these issues significantly improves the efficacy of linear embeddings for BO on a range of problems, including learning a gait policy for robot locomotion.