Abstract:Let F n,d be the class of all functions f : {−1, 1} n → [−1, 1] on the n-dimensional discrete hypercube of degree at most d. In the first part of this paper, we prove that any (deterministic or randomized) algorithm which learns F n,d with L 2 -accuracy ε requires at least Ω((1 − √ ε)2 d log n) queries for large enough n, thus establishing the sharpness as n → ∞ of a recent upper bound of Eskenazis and Ivanisvili (2021). To do this, we show that the L 2 -packing numbers2 Cd log n ε 4 for large enough n, where… Show more
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