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Adversarially Robust Optimization with Gaussian Processes
Ilija Bogunovic · Jonathan Scarlett · Stefanie Jegelka · Volkan Cevher

Wed Dec 05 02:00 PM -- 04:00 PM (PST) @ Room 210 #24

In this paper, we consider the problem of Gaussian process (GP) optimization with an added robustness requirement: The returned point may be perturbed by an adversary, and we require the function value to remain as high as possible even after this perturbation. This problem is motivated by settings in which the underlying functions during optimization and implementation stages are different, or when one is interested in finding an entire region of good inputs rather than only a single point. We show that standard GP optimization algorithms do not exhibit the desired robustness properties, and provide a novel confidence-bound based algorithm StableOpt for this purpose. We rigorously establish the required number of samples for StableOpt to find a near-optimal point, and we complement this guarantee with an algorithm-independent lower bound. We experimentally demonstrate several potential applications of interest using real-world data sets, and we show that StableOpt consistently succeeds in finding a stable maximizer where several baseline methods fail.

Author Information

Ilija Bogunovic (EPFL Lausanne)
Jonathan Scarlett (National University of Singapore)
Stefanie Jegelka (MIT)

Stefanie Jegelka is an X-Consortium Career Development Assistant Professor in the Department of EECS at MIT. She is a member of the Computer Science and AI Lab (CSAIL), the Center for Statistics and an affiliate of the Institute for Data, Systems and Society and the Operations Research Center. Before joining MIT, she was a postdoctoral researcher at UC Berkeley, and obtained her PhD from ETH Zurich and the Max Planck Institute for Intelligent Systems. Stefanie has received a Sloan Research Fellowship, an NSF CAREER Award, a DARPA Young Faculty Award, the German Pattern Recognition Award and a Best Paper Award at the International Conference for Machine Learning (ICML). Her research interests span the theory and practice of algorithmic machine learning.

Volkan Cevher (EPFL)

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