Simultaneous private learning of multiple concepts

Mark Bun, Kobbi Nissim, Uri Stemmer

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


We investigate the direct-sum problem in the context of differentially private PAC learning: What is the sample complexity of solving k learning tasks simultaneously under differential privacy, and how does this cost compare to that of solving k learning tasks without privacy? In our setting, an individual example consists of a domain element x labeled by k unknown concepts (c1; : : : ; ck). The goal of a multi-learner is to output k hypotheses (h1; : : : ; hk) that generalize the input examples. Without concern for privacy, the sample complexity needed to simultaneously learn k concepts is essentially the same as needed for learning a single concept. Under differential privacy, the basic strategy of learning each hypothesis independently yields sample complexity that grows polynomially with k. For some concept classes, we give multi-learners that require fewer samples than the basic strategy. Unfortunately, however, we also give lower bounds showing that even for very simple concept classes, the sample cost of private multi-learning must grow polynomially in k.

Original languageEnglish
JournalJournal of Machine Learning Research
StatePublished - 1 Jun 2019


  • Agnostic learning
  • Differential privacy
  • Direct-sum
  • PAC learning

ASJC Scopus subject areas

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


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