Respecting the limit:Bayesian optimization with a bound on the optimal value

TL;DR

This paper introduces bound-aware Bayesian optimization (BABO), a novel approach that leverages prior knowledge of the optimal value or its bounds to improve optimization efficiency, outperforming existing methods.

Contribution

The paper proposes SlogGP, a new surrogate model that incorporates bound information into Bayesian optimization, enhancing performance even without prior bounds.

Findings

BABO outperforms existing techniques on benchmark problems.

SlogGP improves optimization performance even without prior bound information.

The new surrogate model is more expressive than standard Gaussian processes.

Abstract

In many real-world optimization problems, we have prior information about what objective function values are achievable. In this paper, we study the scenario that we have either exact knowledge of the minimum value or a, possibly inexact, lower bound on its value. We propose bound-aware Bayesian optimization (BABO), a Bayesian optimization method that uses a new surrogate model and acquisition function to utilize such prior information. We present SlogGP, a new surrogate model that incorporates bound information and adapts the Expected Improvement (EI) acquisition function accordingly. Empirical results on a variety of benchmarks demonstrate the benefit of taking prior information about the optimal value into account, and that the proposed approach significantly outperforms existing techniques. Furthermore, we notice that even in the absence of prior information on the bound, the proposed SlogGP surrogate model still performs better than the standard GP model in most cases, which we explain by its larger expressiveness.