Agnostic learning by refuting

Pravesh Kumar Kothari, Roi Livni

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Abstract

The sample complexity of learning a Boolean-valued function class is precisely characterized by its Rademacher complexity. This has little bearing, however, on the sample complexity of efficient agnostic learning. We introduce refutation complexity, a natural computational analog of Rademacher complexity of a Boolean concept class and show that it exactly characterizes the sample complexity of efficient agnostic learning. Informally, refutation complexity of a class C is the minimum number of example-label pairs required to efficiently distinguish between the case that the labels correlate with the evaluation of some member of C (structure) and the case where the labels are i.i.d. Rademacher random variables (noise). The easy direction of this relationship was implicitly used in the recent framework for improper PAC learning lower bounds of Daniely and co-authors [6, 8, 10] via connections to the hardness of refuting random constraint satisfaction problems. Our work can be seen as making the relationship between agnostic learning and refutation implicit in their work into an explicit equivalence. In a recent, independent work, Salil Vadhan [25] discovered a similar relationship between refutation and PAC-learning in the realizable (i.e. noiseless) case.

Original languageEnglish (US)
Title of host publication9th Innovations in Theoretical Computer Science, ITCS 2018
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Volume94
ISBN (Electronic)9783959770606
DOIs
StatePublished - Jan 1 2018
Event9th Innovations in Theoretical Computer Science, ITCS 2018 - Cambridge, United States
Duration: Jan 11 2018Jan 14 2018

Other

Other9th Innovations in Theoretical Computer Science, ITCS 2018
CountryUnited States
CityCambridge
Period1/11/181/14/18

All Science Journal Classification (ASJC) codes

  • Software

Fingerprint Dive into the research topics of 'Agnostic learning by refuting'. Together they form a unique fingerprint.

  • Cite this

    Kothari, P. K., & Livni, R. (2018). Agnostic learning by refuting. In 9th Innovations in Theoretical Computer Science, ITCS 2018 (Vol. 94). [55] Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.ITCS.2018.55