Learning Boolean Halfspaces with Small Weights from Membership Queries
This work addresses a theoretical learning theory problem, providing improved query complexity bounds for researchers in computational learning.
The paper tackles the problem of properly learning Boolean halfspaces with small integer weights from membership queries, closing a gap by presenting an adaptive algorithm that asks n^{O(t)} queries, improving from the previous best of n^{O(t^5)} queries.
We consider the problem of proper learning a Boolean Halfspace with integer weights $\{0,1,\ldots,t\}$ from membership queries only. The best known algorithm for this problem is an adaptive algorithm that asks $n^{O(t^5)}$ membership queries where the best lower bound for the number of membership queries is $n^t$ [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 $n^{O(t)}$ membership queries. We also give a non-adaptive proper learning algorithm that asks $n^{O(t^3)}$ membership queries.