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.
@InProceedings{bshouty:LIPIcs.STACS.2023.16, author = {Bshouty, Nader H.}, title = {{Non-Adaptive Proper Learning Polynomials}}, booktitle = {40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)}, pages = {16:1--16:20}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-266-2}, ISSN = {1868-8969}, year = {2023}, volume = {254}, editor = {Berenbrink, Petra and Bouyer, Patricia and Dawar, Anuj and Kant\'{e}, Mamadou Moustapha}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2023.16}, URN = {urn:nbn:de:0030-drops-176689}, doi = {10.4230/LIPIcs.STACS.2023.16}, annote = {Keywords: Polynomial, Learning, Testing} }
Feedback for Dagstuhl Publishing