We consider the problem of sequentially optimizing a time-varying objective function using time-varying Bayesian optimization (TVBO). Here, the key challenge is the exploration-exploitation trade-off under time variations. Current approaches to TVBO require prior knowledge of a constant rate of change. However, the rate of change is usually neither known nor constant. We propose an event-triggered algorithm, ET-GP-UCB, that treats the optimization problem as static until it detects changes in the objective function online and then resets the dataset. This allows the algorithm to adapt to realized temporal changes without the need for prior knowledge. The event-trigger is based on probabilistic uniform error bounds used in Gaussian process regression. We provide regret bounds for ET-GP-UCB and show in numerical experiments that it is competitive with state-of-the-art algorithms even though it requires no knowledge about the temporal changes. Further, ET-GP-UCB outperforms these baselines if the rate of change is misspecified, and we demonstrate that it is readily applicable to various settings without tuning hyperparameters.

翻译：我们研究了使用时变贝叶斯优化（TVBO）对时变目标函数进行序贯优化的问题。在此过程中，关键挑战在于时变条件下的探索-利用权衡。当前TVBO方法需要预先知道恒定的变化率，然而变化率通常既未知也非常数。我们提出了一种事件触发算法ET-GP-UCB，该算法将优化问题视为静态问题，直到在线检测到目标函数发生变化，随后重置数据集。这使得算法无需先验知识即可自适应实际的时间变化。事件触发机制基于高斯过程回归中使用的概率性均匀误差界。我们为ET-GP-UCB提供了遗憾界，并通过数值实验证明，尽管该算法无需关于时间变化的任何知识，仍能与最先进算法相媲美。此外，若变化率设定错误，ET-GP-UCB的表现优于这些基线方法，同时我们证明该算法无需调整超参数即可直接适用于多种场景。