#### Beyond Perturbations: Learning Guarantees with Arbitrary Adversarial Test Examples

Part of Advances in Neural Information Processing Systems 33 (NeurIPS 2020)

#### Authors

*Shafi Goldwasser, Adam Tauman Kalai, Yael Kalai, Omar Montasser*

#### Abstract

We present a transductive learning algorithm that takes as input training examples
from a distribution P and arbitrary (unlabeled) test examples, possibly chosen by
an adversary. This is unlike prior work that assumes that test examples are small
perturbations of P. Our algorithm outputs a selective classifier, which abstains from predicting on some examples. By considering selective transductive learning, we give the first nontrivial guarantees for learning classes of bounded VC dimension with arbitrary train and test distributionsâ€”no prior guarantees were known even for simple classes of functions such as intervals on the line. In particular, for any function in a class C of bounded VC dimension, we guarantee a low test error rate and a low rejection rate with respect to P. Our algorithm is efficient given an Empirical Risk Minimizer (ERM) for C. Our guarantees hold even for test examples chosen by an unbounded white-box adversary. We also give guarantees for generalization, agnostic, and unsupervised settings.