We consider the problem of proper learning a Boolean Halfspace with integer
weights {0,1,β¦,t} from membership queries only. The best known
algorithm for this problem is an adaptive algorithm that asks nO(t5)
membership queries where the best lower bound for the number of membership
queries is nt [Learning Threshold Functions with Small Weights Using
Membership Queries. COLT 1999]
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(t3) membership
queries