eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-03-03
16:1
16:20
10.4230/LIPIcs.STACS.2023.16
article
Non-Adaptive Proper Learning Polynomials
Bshouty, Nader H.
1
Department of Computer Science, Technion, Haifa, Israel
We give the first polynomial-time non-adaptive proper learning algorithm of Boolean sparse multivariate polynomial under the uniform distribution. Our algorithm, for s-sparse polynomial over n variables, makes q = (s/ε)^{γ(s,ε)}log n queries where 2.66 ≤ γ(s,ε) ≤ 6.922 and runs in Õ(n)⋅ poly(s,1/ε) time. We also show that for any ε = 1/s^{O(1)} any non-adaptive learning algorithm must make at least (s/ε)^{Ω(1)}log n queries. Therefore, the query complexity of our algorithm is also polynomial in the optimal query complexity and optimal in n.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol254-stacs2023/LIPIcs.STACS.2023.16/LIPIcs.STACS.2023.16.pdf
Polynomial
Learning
Testing