Learning Boolean Halfspaces with Small Weights from Membership Queries

Authors: Hasan Abasi, Ali Z. Abdi, and Nader H. Bshouty

Source: Algorithmic Learning Theory, 25th International Conference, ALT 2014, Bled, Slovenia, October 8 - 10, 2014, Proccedings,
Lecture Notes in Artificial Intelligence 8776, pp. 96–110, Springer, 2014.

Abstract. We consider the problem of proper learning a Boolean Halfspace with integer weights {0,1,…,t} from membership queries only. The best known algorithm for this problem is an adaptive algorithm that asks nO(t 5) membership queries where the best lower bound for the number of membership queries is nt (see [AAB99]). In this paper we close this gap and give an adaptive proper learning algorithm with two rounds that asks nO(t) membership queries. We also give a non-adaptive proper learning algorithm that asks nO(t 3) membership queries.

[AAB99]: Abboud, E., Agha, N., Bshouty, N.H., Radwan, N., Saleh, F.: Learning Threshold Functions with Small Weights Using Membership Queries. In: COLT 1999. pp. 318-322 (1999)

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