4 research outputs found
Safety guarantees for iterative predictions with Gaussian Processes
Gaussian Processes (GPs) are widely employed in
control and learning because of their principled treatment of
uncertainty. However, tracking uncertainty for iterative, multistep predictions in general leads to an analytically intractable
problem. While approximation methods exist, they do not
come with guarantees, making it difficult to estimate their
reliability and to trust their predictions. In this work, we derive
formal probability error bounds for iterative predictions with
GPs. Building on GP properties, we bound the probability
that random trajectories lie in specific regions around the
predicted values. Namely, given a tolerance � > 0, we compute
regions around the predicted trajectory values, such that GP
trajectories are guaranteed to lie inside them with probability
at least 1 − �. We verify experimentally that our method
tracks the predictive uncertainty correctly, even when current
approximation techniques fail. Furthermore, we show how the
proposed bounds can incorporate a given control law, and
effectively bound the trajectories of the closed-loop system