Event-Triggered Time-Varying Bayesian Optimization

TL;DR

This paper introduces ET-GP-UCB, an event-triggered Bayesian optimization algorithm that adaptively resets its dataset upon detecting changes in a time-varying objective, eliminating the need for prior knowledge of change rates.

Contribution

The paper proposes a novel event-triggered approach for time-varying Bayesian optimization that adapts online without prior change rate knowledge, with proven regret bounds and superior empirical performance.

Findings

ET-GP-UCB outperforms existing methods on synthetic data.

The algorithm effectively detects changes without prior rate knowledge.

It demonstrates robustness and ease of use in real-world scenarios.

Abstract

We consider the problem of sequentially optimizing a time-varying objective function using time-varying Bayesian optimization (TVBO). Current approaches to TVBO require prior knowledge of a constant rate of change to cope with stale data arising from time variations. 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 and then resets the dataset. This allows the algorithm to adapt online to realized temporal changes without the need for exact prior knowledge. The event trigger is based on probabilistic uniform error bounds used in Gaussian process regression. We derive regret bounds for adaptive resets without exact prior knowledge of the temporal changes and show in numerical experiments that ET-GP-UCB outperforms competing GP-UCB algorithms on both synthetic and real-world data. The results demonstrate that ET-GP-UCB is readily applicable without extensive hyperparameter tuning.