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

• URL: http://arxiv.org/abs/2405.14540v2
• Date: Mon, 21 Oct 2024 16:40:09 GMT
• Title: This Too Shall Pass: Removing Stale Observations in Dynamic Bayesian Optimization
• Authors: Anthony Bardou, Patrick Thiran, Giovanni Ranieri,
• Abstract summary: We build a DBO algorithm able to remove irrelevant observations from its dataset on the fly. We establish the superiority of W-DBO, which outperforms state-of-the-art methods by a comfortable margin.
• Score: 4.6481096949408105
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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