eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-09-04
34:1
34:20
10.4230/LIPIcs.APPROX/RANDOM.2023.34
article
Superpolynomial Lower Bounds for Learning Monotone Classes
Bshouty, Nader H.
1
Department of Computer Science, Technion, Haifa, Israel
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol275-approx-random2023/LIPIcs.APPROX-RANDOM.2023.34/LIPIcs.APPROX-RANDOM.2023.34.pdf
PAC Learning
Monotone DNF
Monotone Decision Tree
Monotone Junta
Lower Bound