This Too Shall Pass: Removing Stale Observations in Dynamic Bayesian Optimization
<|reference_start|>This Too Shall Pass: Removing Stale Observations in Dynamic Bayesian Optimization: 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.<|reference_end|>
@article{bardou2024this,
    title={This Too Shall Pass: Removing Stale Observations in Dynamic Bayesian
  Optimization},
    author={Anthony Bardou, Patrick Thiran, Giovanni Ranieri},
    journal={arXiv preprint arXiv:2405.14540},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.14540},
    primaryClass={stat.ML cs.LG}
}