From tolerant natural properties to tolerant testers

Ascertain whether the existence of a tolerant natural property against a concept class C implies the existence of a tolerant tester for C with comparable parameters, despite the stricter rejection criterion required by tolerant testing.

Background

The paper leverages both tolerant testing and tolerant natural properties in constructing PAC‑verification protocols and remarks on their differing guarantees.

While tolerant testers directly yield distance approximations, tolerant natural properties provide constructive average‑case lower bounds; whether one implies the other remains unclear, with prior work deriving tolerant testing only from proper agnostic learners.