Learning boolean halfspaces with small weights from membership queries

We consider the problem of proper learning of 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(t5) membership queries, while the best lower bound for the number of membership queries is nΩ(t)[1]. In this paper we close this gap and give an adaptive proper learning algorithm with two rounds, and asking nO(t) membership queries. We also give a non-adaptive proper learning algorithm that asks nO(t3) membership queries.