On the Power of Interactive Proofs for Learning

arXiv:2404.08158v1 Announce Type: cross
Abstract: We continue the study of doubly-efficient proof systems for verifying agnostic PAC learning, for which we obtain the following results.
- We construct an interactive protocol for learning the $t$ largest Fourier characters of a given function $f \colon \{0,1\}^n \to \{0,1\}$ up to an arbitrarily small error, wherein the verifier uses $\mathsf{poly}(t)$ random examples. This improves upon the Interactive Goldreich-Levin protocol of Goldwasser, Rothblum, Shafer, and Yehudayoff (ITCS 2021) whose sample complexity is $\mathsf{poly}(t,n)$. …

abstract arxiv characters construct cs.cc cs.ds cs.lg fourier function interactive power protocol results small study systems type