TY - GEN

T1 - Properly learning monotone functions via local correction

AU - Lange, Jane

AU - Rubinfeld, Ronitt

AU - Vasilyan, Arsen

N1 - Publisher Copyright:
© 2022 IEEE.

PY - 2022

Y1 - 2022

N2 - 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.

AB - 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.

KW - local computation algorithms

KW - local reconstruction

KW - monotone functions

KW - proper learning

KW - property testing

UR - http://www.scopus.com/inward/record.url?scp=85146349361&partnerID=8YFLogxK

U2 - 10.1109/FOCS54457.2022.00015

DO - 10.1109/FOCS54457.2022.00015

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???

AN - SCOPUS:85146349361

T3 - Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS

SP - 75

EP - 86

BT - Proceedings - 2022 IEEE 63rd Annual Symposium on Foundations of Computer Science, FOCS 2022

PB - IEEE Computer Society

Y2 - 31 October 2022 through 3 November 2022

ER -