On Fundamental Limits of Robust Learning

Abstract

We consider the problems of robust PAC learning from distributed and streaming data, which may contain malicious errors and outliers, and analyze their fundamental complexity questions. In particular, we establish lower bounds on the communication complexity for distributed robust learning performed on multiple machines, and on the space complexity for robust learning from streaming data on a single machine. These results demonstrate that gaining robustness of learning algorithms is usually at the expense of increased complexities. As far as we know, this work gives the first complexity results for distributed and online robust PAC learning.

On the Sample Complexity of Adversarial Multi-Source PAC Learning

“…However, they only focus on label corruptions. Feng (2017) consider the fundamental limits of learning from adversarial distributed data, but in the case when each of the nodes can iteratively send corrupted updates with certain probability. Feng et al (2014) provide a method for distributing the computation of any robust learning algorithm that operates on a single large dataset.…”