Properly learning monotone functions via local correction

Jane Lange, Ronitt Rubinfeld, Arsen Vasilyan

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


We give a 2O(vn/?)-time algorithm for properly learning monotone Boolean functions under the uniform distribution over {0,1}n. Our algorithm is robust to adversarial label noise and has a running time nearly matching that of the state-of-the-art improper learning algorithm of Bshouty and Tamon (JACM 96) and an information-theoretic lower bound of Blais et al (RANDOM '15). Prior to this work, no proper learning algorithm with running time smaller than 2O(n) was known to exist. The core of our proper learner is a local computation algorithm for sorting binary labels on a poset. Our algorithm is built on a body of work on distributed greedy graph algorithms; specifically we rely on a recent work of Ghaffari (FOCS'22), which gives an efficient algorithm for computing maximal matchings in a graph in the LCA model of Rubinfeld et al and Alon et al (ICS'II, SODA'12). The applications of our local sorting algorithm extend beyond learning on the Boolean cube: we also give a tolerant tester for Boolean functions over general posets that distinguishes functions that are ?/3-close to monotone from those that are ?-far. Previous tolerant testers for the Boolean cube only distinguished between ?/O(vn)-close and ?-far.

Original languageEnglish
Title of host publicationProceedings - 2022 IEEE 63rd Annual Symposium on Foundations of Computer Science, FOCS 2022
PublisherIEEE Computer Society
Number of pages12
ISBN (Electronic)9781665455190
StatePublished - 2022
Externally publishedYes
Event63rd IEEE Annual Symposium on Foundations of Computer Science, FOCS 2022 - Denver, United States
Duration: 31 Oct 20223 Nov 2022

Publication series

NameProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
ISSN (Print)0272-5428


Conference63rd IEEE Annual Symposium on Foundations of Computer Science, FOCS 2022
Country/TerritoryUnited States


  • local computation algorithms
  • local reconstruction
  • monotone functions
  • proper learning
  • property testing


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