Re-Examining Linear Embeddings for High-Dimensional Bayesian Optimization
This work addresses sample efficiency in high-dimensional Bayesian optimization, but it is incremental as it builds on existing linear embedding methods.
The paper tackled the problem of scaling Bayesian optimization to high-dimensional spaces by identifying and addressing issues with linear embeddings, showing that proper design choices significantly improve performance on tasks like robot locomotion.
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.