Bayesian Multi-Scale Optimistic Optimization

TL;DR

This paper introduces a new Bayesian optimization method that combines Gaussian process confidence bounds with optimistic optimization, eliminating the need for costly auxiliary optimization and providing finite-time convergence guarantees.

Contribution

It presents a novel approach that removes the requirement for auxiliary optimization in Bayesian optimization, improving efficiency and theoretical convergence analysis.

Findings

More efficient than traditional Bayesian optimization methods

Provides finite-time convergence rate proofs without exact acquisition optimization

Demonstrates effectiveness on benchmarks and real-world applications

Abstract

Bayesian optimization is a powerful global optimization technique for expensive black-box functions. One of its shortcomings is that it requires auxiliary optimization of an acquisition function at each iteration. This auxiliary optimization can be costly and very hard to carry out in practice. Moreover, it creates serious theoretical concerns, as most of the convergence results assume that the exact optimum of the acquisition function can be found. In this paper, we introduce a new technique for efficient global optimization that combines Gaussian process confidence bounds and treed simultaneous optimistic optimization to eliminate the need for auxiliary optimization of acquisition functions. The experiments with global optimization benchmarks and a novel application to automatic information extraction demonstrate that the resulting technique is more efficient than the two approaches from which it draws inspiration. Unlike most theoretical analyses of Bayesian optimization with Gaussian processes, our finite-time convergence rate proofs do not require exact optimization of an acquisition function. That is, our approach eliminates the unsatisfactory assumption that a difficult, potentially NP-hard, problem has to be solved in order to obtain vanishing regret rates.