Non-Adaptive Proper Learning Polynomials

We give the first polynomial-time non-adaptive proper learning algorithm of Boolean sparse multivariate polynomial under the uniform distribution. Our algorithm, for s -sparse polynomial over n variables, makes q = ( s/ϵ ) γ ( s,ϵ ) log n queries where 2 . 66 ≤ γ ( s, ϵ ) ≤ 6 . 922 and runs in ˜ O ( n ) · poly ( s, 1 /ϵ ) time. We also show that for any ϵ = 1 /s O (1) any non-adaptive learning algorithm must make at least ( s/ϵ ) Ω(1) log n queries. Therefore, the query complexity of our algorithm is also polynomial in the optimal query complexity and optimal in n .