On Fundamental Limits of Robust Learning

TL;DR

This paper investigates the fundamental complexity limits of robust PAC learning in distributed and streaming settings, revealing that achieving robustness often incurs higher communication and space costs.

Contribution

It provides the first known lower bounds on communication and space complexity for distributed and streaming robust PAC learning.

Findings

Lower bounds on communication complexity for distributed robust learning

Lower bounds on space complexity for streaming robust learning

Robustness in learning algorithms generally increases complexity

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.