Learners that Use Little Information

Raef Bassily, Shay Moran, Ido Nachum, Jonathan Shafer, Amir Yehudayoff

Research output: Contribution to journalConference articlepeer-review


We study learning algorithms that are restricted to using a small amount of information from their input sample. We introduce a category of learning algorithms we term d-bit information learners, which are algorithms whose output conveys at most d bits of information of their input. A central theme in this work is that such algorithms generalize. We focus on the learning capacity of these algorithms, and prove sample complexity bounds with tight dependencies on the confidence and error parameters. We also observe connections with well studied notions such as sample compression schemes, Occam’s razor, PAC-Bayes and differential privacy. We discuss an approach that allows us to prove upper bounds on the amount of information that algorithms reveal about their inputs, and also provide a lower bound by showing a simple concept class for which every (possibly randomized) empirical risk minimizer must reveal a lot of information. On the other hand, we show that in the distribution-dependent setting every VC class has empirical risk minimizers that do not reveal a lot of information.

Original languageEnglish
Pages (from-to)25-55
Number of pages31
JournalProceedings of Machine Learning Research
StatePublished - 2018
Externally publishedYes
Event29th International Conference on Algorithmic Learning Theory, ALT 2018 - Lanzarote, Spain
Duration: 7 Apr 20189 Apr 2018

Bibliographical note

Publisher Copyright:
© 2018 Raef Bassily, Shay Moran, Ido Nachum, Jonathan Shafer and Amir Yehudayoff.


  • Compression
  • Differential Privacy
  • Information Theory
  • Occam’s Razor
  • PAC Learning
  • PAC-Bayes
  • Sample Compression Scheme

ASJC Scopus subject areas

  • Artificial Intelligence
  • Software
  • Control and Systems Engineering
  • Statistics and Probability


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