Bayesian Optimization using Pseudo-Points

TL;DR

This paper introduces a novel Bayesian optimization framework that enhances Gaussian process models by generating pseudo-points, leading to improved optimization performance on various problems.

Contribution

It proposes a general pseudo-point generation framework for Bayesian optimization, with theoretical regret bounds and demonstrated empirical advantages.

Findings

Pseudo-points improve Gaussian process modeling in BO.

Theoretical regret bounds are established for the proposed method.

Empirical results show enhanced optimization performance with pseudo-points.

Abstract

Bayesian optimization (BO) is a popular approach for expensive black-box optimization, with applications including parameter tuning, experimental design, robotics. BO usually models the objective function by a Gaussian process (GP), and iteratively samples the next data point by maximizing an acquisition function. In this paper, we propose a new general framework for BO by generating pseudo-points (i.e., data points whose objective values are not evaluated) to improve the GP model. With the classic acquisition function, i.e., upper confidence bound (UCB), we prove that the cumulative regret can be generally upper bounded. Experiments using UCB and other acquisition functions, i.e., probability of improvement (PI) and expectation of improvement (EI), on synthetic as well as real-world problems clearly show the advantage of generating pseudo-points.