A note on learning multivariate polynomials under the uniform distribution (extended abstract)

We present a PAC-leaming algorithm with membership queries for learning any multivariate polynomial over any finite field f under the uniform distribution. The atgorithm runs in time 1 queries where t is the number of terms in the polynomial, 71is the number of variables and IFl is the field size. This complexity is polynomial for any fix finite field Y. The output hypothesis is a multivariate polynomial with less than or equal to t terms. We also show that O(log n)-multivariate polynomials (each term contains at most O (log n) distinct variables) are exactly learnable from membership and equivalence queries in time n“(’og I‘11. Nader H. Bshouty