TY - GEN
T1 - Active Learning Polynomial Threshold Functions
AU - Ben-Eliezer, Omri
AU - Hopkins, Max
AU - Yang, Chutong
AU - Yu, Hantao
N1 - Publisher Copyright:
© 2022 Neural information processing systems foundation. All rights reserved.
PY - 2022
Y1 - 2022
N2 - We initiate the study of active learning polynomial threshold functions (PTFs). While traditional lower bounds imply that even univariate quadratics cannot be non-trivially actively learned, we show that allowing the learner basic access to the derivatives of the underlying classifier circumvents this issue and leads to a computationally efficient algorithm for active learning degree-d univariate PTFs in Õ(d3 log(1/εδ)) queries. We extend this result to the batch active setting, providing a smooth transition between query complexity and rounds of adaptivity, and also provide near-optimal algorithms for active learning PTFs in several average case settings. Finally, we prove that access to derivatives is insufficient for active learning multivariate PTFs, even those of just two variables.
AB - We initiate the study of active learning polynomial threshold functions (PTFs). While traditional lower bounds imply that even univariate quadratics cannot be non-trivially actively learned, we show that allowing the learner basic access to the derivatives of the underlying classifier circumvents this issue and leads to a computationally efficient algorithm for active learning degree-d univariate PTFs in Õ(d3 log(1/εδ)) queries. We extend this result to the batch active setting, providing a smooth transition between query complexity and rounds of adaptivity, and also provide near-optimal algorithms for active learning PTFs in several average case settings. Finally, we prove that access to derivatives is insufficient for active learning multivariate PTFs, even those of just two variables.
UR - http://www.scopus.com/inward/record.url?scp=85163190100&partnerID=8YFLogxK
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AN - SCOPUS:85163190100
T3 - Advances in Neural Information Processing Systems
BT - Advances in Neural Information Processing Systems 35 - 36th Conference on Neural Information Processing Systems, NeurIPS 2022
A2 - Koyejo, S.
A2 - Mohamed, S.
A2 - Agarwal, A.
A2 - Belgrave, D.
A2 - Cho, K.
A2 - Oh, A.
PB - Neural information processing systems foundation
T2 - 36th Conference on Neural Information Processing Systems, NeurIPS 2022
Y2 - 28 November 2022 through 9 December 2022
ER -