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This research advances Time-Varying Bayesian Optimization by removing the unrealistic constraint of constant sampling frequencies, addressing a critical bottleneck where Gaussian Process complexity scales cubically with dataset size. By deriving new regret bounds that account for variable observation rates, the authors introduce practical guidelines for managing stale data and dataset sizing in dynamic environments. The proposed BOLT algorithm demonstrates superior performance over current state-of-the-art methods on both synthetic benchmarks and real-world applications, offering a more robust framework for optimizing expensive black-box functions under non-stationary conditions.
Time-Varying Bayesian Optimization Without a Metronome
arXiv:2501.18963v4 Announce Type: replace-cross Abstract: Time-Varying Bayesian Optimization (TVBO) is the go-to framework for optimizing a time-varying, expensive, noisy black-box function $f$. However, most of the asymptotic guarantees offered by TVBO algorithms rely on the assumption that observations are acquired at a constant frequency. As the GP inference complexity scales with the cube of its dataset size, this assumption is unrealistic in the long run. In this paper, we relax this assumption and derive the first upper regret bound that explicitly accounts for changes in the observations sampling frequency. Based on this analysis, we formulate practical recommendations about dataset sizes and stale data policies of TVBO algorithms. We illustrate how an algorithm (BOLT) that follows these recommendations performs better than the state-of-the-art of TVBO through experiments on synthetic and real-world problems.
Abstract:Time-Varying Bayesian Optimization (TVBO) is the go-to framework for optimizing a time-varying, expensive, noisy black-box function $f$. However, most of the asymptotic guarantees offered by TVBO algorithms rely on the assumption that observations are acquired at a constant frequency. As the GP inference complexity scales with the cube of its dataset size, this assumption is unrealistic in the long run. In this paper, we relax this assumption and derive the first upper regret bound that explicitly accounts for changes in the observations sampling frequency. Based on this analysis, we formulate practical recommendations about dataset sizes and stale data policies of TVBO algorithms. We illustrate how an algorithm (BOLT) that follows these recommendations performs better than the state-of-the-art of TVBO through experiments on synthetic and real-world problems.
Machine Learning (stat.ML); Machine Learning (cs.LG)
arXiv:2501.18963 [stat.ML]
(or arXiv:2501.18963v4 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2501.18963 Focus to learn more arXiv-issued DOI via DataCite
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