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.

On Controller Tuning with Time-Varying Bayesian Optimization

Changing conditions or environments can cause system dynamics to vary over time. To ensure optimal control performance, controllers should adapt to these changes. When the underlying cause and time of change is unknown, we need to rely on online data for this adaptation. In this paper, we will use time-varying Bayesian optimization (TVBO) to tune controllers online in changing environments using appropriate prior knowledge on the control objective and its changes. Two properties are characteristic of many online controller tuning problems: First, they exhibit incremental and lasting changes in the objective due to changes to the system dynamics, e.g., through wear and tear. Second, the optimization problem is convex in the tuning parameters. Current TVBO methods do not explicitly account for these properties, resulting in poor tuning performance and many unstable controllers through over-exploration of the parameter space. We propose a novel TVBO forgetting strategy using Uncertainty-Injection (UI), which incorporates the assumption of incremental and lasting changes. The control objective is modeled as a spatio-temporal Gaussian process (GP) with UI through a Wiener process in the temporal domain. Further, we explicitly model the convexity assumptions in the spatial dimension through GP models with linear inequality constraints. In numerical experiments, we show that our model outperforms the state-of-the-art method in TVBO, exhibiting reduced regret and fewer unstable parameter configurations.