Title:

Learning with Local and Global Adversarial Corruptions

Abstract: 

We study learning in an adversarial setting, where an epsilon fraction of samples from a distribution P are globally corrupted (arbitrarily modified), and the remaining perturbations have an average magnitude bounded by rho (local corruptions). With access to n such corrupted samples, we aim to develop a computationally efficient approach that achieves the optimal minimax excess risk. Our approach combines a data-driven cleaning module with a distributionally robust optimization (DRO) framework. We demonstrate that if the data cleaning module is minimax optimal with respect to the Wasserstein loss, solving an optimal transport-based DRO problem ensures a minimax optimal decision. We further provide tractable reformulations for both modules. Specifically, we introduce an optimal filtering algorithm to clean corrupted data by identifying and removing outliers. For the DRO module, we reformulate the problem as a two-player zero-sum game, deriving finite convex formulations. We show that the minimax theorem applies to this game, and Nash equilibria exist. Finally, we present a principled approach for constructing adversarial examples.

Bio: 

Soroosh Shafiee is an assistant professor in the School of Operations Research and Information Engineering at Cornell University. Before that, he held positions as a postdoctoral researcher at both the Tepper School of Business at Carnegie Mellon University and the Automatic Control Laboratory at ETH Zurich. He held a B.Sc. and M.Sc. degree in Electrical Engineering from the University of Tehran and a Ph.D. degree in Operations Research from EPFL. His primary research interests revolve around data-driven optimization, low-complexity decision-making and optimal transport.