Transferring IPP query-to-sample reductions to PAC-verification

Determine whether the sample-based query-to-sample reductions developed for interactive proofs of proximity can be extended to PAC-verification of agnostic learning tasks without incurring prohibitive (e.g., quadratic) sample-complexity overheads, or develop alternative reductions achieving comparable guarantees.

Background

Interactive proofs of proximity (IPPs) admit query-to-sample reductions (GR’22). The paper’s PAC-verification reductions are tailored to learning-specific query structures and may incur quadratic blow-ups when naively applied to IPPs, risking triviality in interesting regimes.

Clarifying whether IPP techniques can be adapted to PAC-verification, or designing new reductions that avoid such blow-ups, would unify or differentiate these paradigms and improve sample efficiency.