@inproceedings{
chandrasekaran2024efficient,
title={Efficient Discrepancy Testing for Learning with Distribution Shift},
author={Gautam Chandrasekaran and Adam Klivans and Vasilis Kontonis and Konstantinos Stavropoulos and Arsen Vasilyan},
booktitle={The Thirty-eighth Annual Conference on Neural Information Processing Systems},
year={2024},
url={https://openreview.net/forum?id=ojIhvhQBAQ}
}
A fundamental notion of distance between train and test distributions from the field of domain adaptation is discrepancy distance. While in general hard to compute, here we provide the first set of provably efficient algorithms for testing *localized* discrepancy distance, where discrepancy is computed with respect to a fixed output classifier.  These results imply a broad set of new, efficient learning algorithms in the recently introduced model of Testable Learning with Distribution Shift (TDS learning) due to Klivans et al. (2023).

Our approach generalizes and improves all prior work on TDS learning: (1) we obtain *universal* learners that succeed simultaneously for large classes of test distributions, (2) achieve near-optimal error rates, and (3) give exponential improvements for constant depth circuits. Our methods further extend to semi-parametric settings and imply the first positive results for low-dimensional convex sets. Additionally, we separate learning and testing phases and obtain algorithms that run in fully polynomial time at test time.
Efficient Discrepancy Testing for Learning with Distribution Shift
Gautam Chandrasekaran Adam Klivans Vasilis Kontonis Konstantinos Stavropoulos Arsen Vasilyan