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, in practice, the rate of change is usually unknown. 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 outperforms state-of-the-art algorithms on synthetic and real-world data. Furthermore, these results demonstrate that ET-GP-UCB is readily applicable to various settings without tuning hyperparameters.

翻译：我们考虑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，核心挑战在于时变场景下的探索-利用权衡。现有TVBO方法需要预先知道恒定变化率，然而在实际应用中，变化率通常是未知的。我们提出一种事件触发算法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，随即重置数据集。这使得算法能够自适应实际的时间变化，而无需先验知识。该事件触发机制基于高斯过程回归中使用的概率均匀误差界。我们为ET-GP-UCB提供了遗憾界，并通过数值实验证明，在合成数据和真实数据上，该算法性能优于当前最优算法。此外，这些结果表明ET-GP-UCB无需调整超参数即可直接适用于多种场景。