2026-08-07T05:19:32Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:18859 2024-03-06T11:02:45Z ddc:004 open_access

Superpolynomial Lower Bounds for Learning Monotone Classes Bshouty, Nader H. PAC Learning Monotone DNF Monotone Decision Tree Monotone Junta Lower Bound Koch, Strassle, and Tan [SODA 2023], show that, under the randomized exponential time hypothesis, there is no distribution-free PAC-learning algorithm that runs in time n^Õ(log log s) for the classes of n-variable size-s DNF, size-s Decision Tree, and log s-Junta by DNF (that returns a DNF hypothesis). Assuming a natural conjecture on the hardness of set cover, they give the lower bound n^Ω(log s). This matches the best known upper bound for n-variable size-s Decision Tree, and log s-Junta. In this paper, we give the same lower bounds for PAC-learning of n-variable size-s Monotone DNF, size-s Monotone Decision Tree, and Monotone log s-Junta by DNF. This solves the open problem proposed by Koch, Strassle, and Tan and subsumes the above results. The lower bound holds, even if the learner knows the distribution, can draw a sample according to the distribution in polynomial time, and can compute the target function on all the points of the support of the distribution in polynomial time. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Nader H. Bshouty 2023 Is Part Of LIPIcs, Volume 275, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.APPROX/RANDOM.2023.34 urn:nbn:de:0030-drops-188594 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2023.34 eng https://creativecommons.org/licenses/by/4.0/legalcode