Event-Triggered Time-Varying Bayesian Optimization

We consider the problem of sequentially optimizing a time-varying objective function using time-varying Bayesian optimization (TVBO). Here, the key challenge is to cope with old data. 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 detects changes in the objective function online. The event-trigger is based on probabilistic uniform error bounds used in Gaussian process regression. The trigger automatically detects when significant change in the objective functions occurs. The algorithm then adapts to the temporal change by resetting the accumulated dataset. 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 competitive baselines if the rate of change is misspecified and we demonstrate that it is readily applicable to various settings without tuning hyperparameters.