Balancing Proactiveness and Robustness in Online Super Level Set Estimation
Time: 2017-12-19
Published By: Xiaoni Tan
Speaker(s): Junzi Zhang, Ph.D. Candidate, Stanford University
Time: 10:00-11:00 December 20, 2017
Venue: Room 9, Quan Zhai, BICMR
We consider the problem of determining the subregion where a function exceeds a given threshold. This problem of (super) level set estimation arises naturally in the context of safety control, signal coverage, and environmental monitoring, where surpassing a particular value indicates danger, poor communication, or unacceptable pollution levels. Assuming that we only have access to a noise-corrupted version of the function and that function evaluations are super expensive, the problem can be seen as a generalization of Bayesian optimization.To select the next query point, we propose to proactively maximize the expected increase in the area identified as above the threshold as predicted by a Gaussian process, with robustifying corrections to ensure asymptotic convergence on finite grids. We show by numerical experiments that our approach can significantly outperform existing techniques in the literature. This is a joint work with Andrea Zanette, Blake Wulfe and Mykel Kochenderfer.
