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:我们考虑的是使用时间变化的巴伊西亚优化(TVBO)来按顺序优化时间变化目标函数的问题。 这里, 关键的挑战在于时间变化中的探索- 开发权衡。 目前对TVBO的做法需要事先知道一个不变的变动率。 但是,变化率通常既不为人所知,也不为常态。 我们提议一个事件触发算法,即ET-GP-UCB, 将优化问题作为静态处理, 直到它发现在线客观函数的变化, 然后重新配置数据集。 这让算法能够适应已经实现的时间变化, 而不需要事先知道。 事件触发器基于高斯进程回归中使用的概率统一错误界限。 我们为ET- GP-UCB提供了遗憾的界限, 并在数字实验中显示它与最新算法具有竞争力, 尽管它不需要对时间变化的任何了解。 此外, ET- GP- UCB 如果变化率被错误描述, 就会超越这些基线。 我们证明它很容易适用于各种环境, 而没有调整超分辨率 。