DNF Learning via Locally Mixing Random Walks
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3717823.3718262.pdf
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Author(s)
Alman, Josh
Nadimpalli, Shivam
Patel, Shyamal
Servedio, Rocco A.
Date Issued
June 15, 2025
Publisher
ACM|Proceedings of the 57th Annual ACM Symposium on Theory of Computing
Citation
Josh Alman, Shivam Nadimpalli, Shyamal Patel, and Rocco A. Servedio. 2025. DNF Learning via Locally Mixing Random Walks. In Proceedings of the 57th Annual ACM Symposium on Theory of Computing (STOC '25). Association for Computing Machinery, New York, NY, USA, 2055–2061.
Version
Final published version
Abstract
We give two results on PAC learning DNF formulas using membership queries in the challenging “distribution-free” learning framework, where learning algorithms must succeed for an arbitrary and unknown distribution over {0,1}n.
(1) We first give a quasi-polynomial time “list-decoding” algorithm for learning a single term of an unknown DNF formula. More precisely, for any target s-term DNF formula f = T1 ∨ ⋯ ∨ Ts over {0,1}n and any unknown distribution D over {0,1}n, our algorithm, which uses membership queries and random examples from D, runs in quasipoly(n,s) time and outputs a list L of candidate terms such that with high probability some term Ti of f belongs to L.
(2) We then use result (1) to give a quasipoly(n,s)-time algorithm, in the distribution-free PAC learning model with membership queries, for learning the class of size-s DNFs in which all terms have the same size. Our algorithm learns using a DNF hypothesis.
The key tool used to establish result (1) is a new result on “locally mixing random walks,” which, roughly speaking, shows that a random walk on a graph that is covered by a small number of expanders has a non-negligible probability of mixing quickly in a subset of these expanders.
Description
STOC ’25, Prague, Czechia
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1145/3717823.3718262
