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Interactive Proofs for Verifying Machine Learning

Authors Shafi Goldwasser , Guy N. Rothblum , Jonathan Shafer , Amir Yehudayoff

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Author Details

Shafi Goldwasser
  • University of California, Berkeley, CA, USA
Guy N. Rothblum
  • Weizmann Institute of Science, Rehovot, Israel
Jonathan Shafer
  • University of California, Berkeley, CA, USA
Amir Yehudayoff
  • Technion - Israel Institute of Technology, Haifa, Israel

Funding

  • Goldwasser, Shafi: Research was supported in part by DARPA under Contract No. HR001120C0015.
  • Rothblum, Guy N.: This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 819702).
  • Yehudayoff, Amir: Research was supported by ISF grant No. 1162/15.

Acknowledgements

The authors would like to thank Oded Ben-David, Eyal Ben-David, Alessandro Chiesa, Constantinos Daskalakis, Oded Goldreich, Ankur Moitra, Ido Nachum, Orr Paradise and Avishay Tal for insightful discussions and helpful references.

Cite AsGet BibTex

Shafi Goldwasser, Guy N. Rothblum, Jonathan Shafer, and Amir Yehudayoff. Interactive Proofs for Verifying Machine Learning. In 12th Innovations in Theoretical Computer Science Conference (ITCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 185, pp. 41:1-41:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.ITCS.2021.41

Abstract

We consider the following question: using a source of labeled data and interaction with an untrusted prover, what is the complexity of verifying that a given hypothesis is "approximately correct"? We study interactive proof systems for PAC verification, where a verifier that interacts with a prover is required to accept good hypotheses, and reject bad hypotheses. Both the verifier and the prover are efficient and have access to labeled data samples from an unknown distribution. We are interested in cases where the verifier can use significantly less data than is required for (agnostic) PAC learning, or use a substantially cheaper data source (e.g., using only random samples for verification, even though learning requires membership queries). We believe that today, when data and data-driven algorithms are quickly gaining prominence, the question of verifying purported outcomes of data analyses is very well-motivated. We show three main results. First, we prove that for a specific hypothesis class, verification is significantly cheaper than learning in terms of sample complexity, even if the verifier engages with the prover only in a single-round (NP-like) protocol. Moreover, for this class we prove that single-round verification is also significantly cheaper than testing closeness to the class. Second, for the broad class of Fourier-sparse boolean functions, we show a multi-round (IP-like) verification protocol, where the prover uses membership queries, and the verifier is able to assess the result while only using random samples. Third, we show that verification is not always more efficient. Namely, we show a class of functions where verification requires as many samples as learning does, up to a logarithmic factor.

Subject Classification

ACM Subject Classification
  • Theory of computation → Interactive proof systems
  • Theory of computation → Machine learning theory
Keywords
  • PAC learning
  • Fourier analysis of boolean functions
  • Complexity gaps
  • Complexity lower bounds
  • Goldreich-Levin algorithm
  • Kushilevitz-Mansour algorithm
  • Distribution testing

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