This Too Shall Pass: Removing Stale Observations in Dynamic Bayesian Optimization

TL;DR

This paper introduces W-DBO, a dynamic Bayesian optimization method that removes outdated observations using Wasserstein distance, improving performance in continuous-time, dynamic black-box function optimization tasks.

Contribution

The paper proposes a novel Wasserstein distance-based criterion to identify and remove stale observations in dynamic Bayesian optimization, enhancing adaptability and accuracy.

Findings

W-DBO outperforms existing methods in dynamic optimization tasks.

The approach maintains high sampling frequency and predictive accuracy.

Numerical experiments confirm the effectiveness of the proposed method.

Abstract

Bayesian Optimization (BO) has proven to be very successful at optimizing a static, noisy, costly-to-evaluate black-box function $f : \mathcal{S} \to \mathbb{R}$. However, optimizing a black-box which is also a function of time (i.e., a dynamic function) $f : \mathcal{S} \times \mathcal{T} \to \mathbb{R}$ remains a challenge, since a dynamic Bayesian Optimization (DBO) algorithm has to keep track of the optimum over time. This changes the nature of the optimization problem in at least three aspects: (i) querying an arbitrary point in $\mathcal{S} \times \mathcal{T}$ is impossible, (ii) past observations become less and less relevant for keeping track of the optimum as time goes by and (iii) the DBO algorithm must have a high sampling frequency so it can collect enough relevant observations to keep track of the optimum through time. In this paper, we design a Wasserstein distance-based criterion able to quantify the relevancy of an observation with respect to future predictions. Then, we leverage this criterion to build W-DBO, a DBO algorithm able to remove irrelevant observations from its dataset on the fly, thus maintaining simultaneously a good predictive performance and a high sampling frequency, even in continuous-time optimization tasks with unknown horizon. Numerical experiments establish the superiority of W-DBO, which outperforms state-of-the-art methods by a comfortable margin.