Simultaneous O(1/(nt)) error rate across all rounds in contaminated PAC learning

Determine whether, in the iterative PAC learning model where each round t collects n examples from distribution D and labels each example by the previous-round classifier f_{t-1} with probability α and by the true concept f* with probability 1−α, there exists a learning algorithm that achieves generalization error O(1/(n t)) at every round t simultaneously for hypothesis classes with finite VC dimension in the realizable setting.

Background

The paper studies an iterative training loop in which each round’s dataset mixes labels from the true concept and the previous model at rate α. For hypothesis classes with finite VC dimension, Theorem 3 constructs an algorithm achieving a rate on the order of √(d/((1−α)nt)) for all rounds.

In the Discussion, the authors note that an O(1/(nt)) rate can be attained for the final round if one allows earlier rounds to deploy high-error models, thereby collecting more corrective feedback. They explicitly leave open whether the stronger O(1/(nt)) rate can be achieved uniformly for every round while maintaining the requirement of steadily improving models.