Distribution Free Learning with Local Queries

Galit Bary-Weisberg, Amit Daniely, Shai Shalev-Shwartz

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1 Scopus citations


The model of learning with local membership queries interpolates between the PAC model and the membership queries model by allowing the learner to query the label of any example that is similar to an example in the training set. This model, recently proposed and studied by Awasthi et al. (2012), aims to facilitate practical use of membership queries. We continue this line of work, proving both positive and negative results in the distribution free setting. We restrict to the boolean cube {-1, 1}n, and say that a query is q-local if it is of a hamming distance ≤ q from some training example. On the positive side, we show that 1-local queries already give an additional strength, and allow to learn a certain type of DNF formulas, that are not learnable without queries, assuming that learning decision trees is hard. On the negative side, we show that even (n0.99)-local queries cannot help to learn various classes including Automata, DNFs and more. Likewise, q-local queries for any constant q cannot help to learn Juntas, Decision Trees, Sparse Polynomials and more. Moreover, for these classes, an algorithm that uses (log0.99(n))local queries would lead to a breakthrough in the best known running times.

Original languageAmerican English
Pages (from-to)133-147
Number of pages15
JournalProceedings of Machine Learning Research
StatePublished - 2020
Event31st International Conference on Algorithmic Learning Theory, ALT 2020 - San Diego, United States
Duration: 8 Feb 202011 Feb 2020

Bibliographical note

Publisher Copyright:
© 2020 G. Bary-Weisberg, A. Daniely & S. Shalev-Shwartz.


  • DNFs
  • Local Membership Queries
  • PAC Learning


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