Learning low-degree functions from a logarithmic number of random queries

Abstract

We prove that for any integer n ∈ N, d ∈ {1, . . . , n} and any ε, δ ∈ (0, 1), a bounded function f : {−1, 1} n → [−1, 1] of degree at most d can be learned with probability at least 1 − δ and L 2 -error ε using log( n δ ) ε −d−1 C d 3/2 √ log d random queries for a universal finite constant C > 1.