Time-Varying Bayesian Optimization (TVBO) is a common approach for optimizing black-box functions that change over time, especially when evaluations are noisy or expensive. It has shown strong empirical results across applications like robotics and adaptive control, but its theoretical properties have remained largely unexplored. A new paper on arXiv tackles this gap by analyzing the asymptotic performance of TVBO.
The authors focus on regret—the difference between the algorithm's performance and the best possible performance over time—and derive bounds that hold as the number of evaluations grows. These bounds clarify how quickly TVBO converges in dynamic environments and under what conditions it remains effective. The analysis appears to be the first of its kind for this class of time-varying problems.
Because the source is a single preprint, the findings have not yet been peer-reviewed. Still, the work is significant: it moves TVBO from a purely empirical tool to one with formal guarantees, which could guide practitioners in choosing when to rely on it and how to tune its parameters. Future work may extend these results to more general settings or tighter bounds.