Surrogate modeling for Bayesian optimization beyond a single Gaussian process

TL;DR

This paper introduces an ensemble of Gaussian processes for Bayesian optimization, enhancing flexibility and scalability over traditional single-GP models, with proven convergence and practical effectiveness in diverse applications.

Contribution

It proposes a novel ensemble GP model with adaptive selection and Thompson sampling for scalable, parallel Bayesian optimization, surpassing single-GP approaches.

Findings

Enhanced expressiveness with GP ensemble

Scalable parallel optimization via Thompson sampling

Proven convergence through Bayesian regret analysis

Abstract

Bayesian optimization (BO) has well-documented merits for optimizing black-box functions with an expensive evaluation cost. Such functions emerge in applications as diverse as hyperparameter tuning, drug discovery, and robotics. BO hinges on a Bayesian surrogate model to sequentially select query points so as to balance exploration with exploitation of the search space. Most existing works rely on a single Gaussian process (GP) based surrogate model, where the kernel function form is typically preselected using domain knowledge. To bypass such a design process, this paper leverages an ensemble (E) of GPs to adaptively select the surrogate model fit on-the-fly, yielding a GP mixture posterior with enhanced expressiveness for the sought function. Acquisition of the next evaluation input using this EGP-based function posterior is then enabled by Thompson sampling (TS) that requires no additional design parameters. To endow function sampling with scalability, random feature-based kernel approximation is leveraged per GP model. The novel EGP-TS readily accommodates parallel operation. To further establish convergence of the proposed EGP-TS to the global optimum, analysis is conducted based on the notion of Bayesian regret for both sequential and parallel settings. Tests on synthetic functions and real-world applications showcase the merits of the proposed method.