Event-Triggered Time-Varying Bayesian Optimization
We consider the problem of sequentially optimizing a time-varying objective function using time-varying Bayesian optimization (TVBO). To cope with stale data arising from 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 show in numerical experiments that ET-GP-UCB outperforms state-of-the-art algorithms on synthetic and real-world data and provide regret bounds for the proposed algorithm. The results demonstrate that ET-GP-UCB is readily applicable without prior knowledge on the rate of change.
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