Estimating opt_C(f) with a bounded prover in PAC‑verification

Determine whether a verifier, interacting with a computationally bounded prover, can estimate opt_C(f)=min_{c∈C}dist(f,c) for expressive hypothesis classes C within the PAC‑verification framework, thereby enabling verification of near‑optimal hypotheses without relying on unbounded provers.

Background

In realizable learning, a verifier can estimate hypothesis error directly from random examples, but agnostic settings require comparing against the unknown best‑in‑class error opt_C(f).

The paper points out that, for reasonably powerful classes, it is unclear how to estimate opt_C(f) with only a bounded prover, highlighting a central obstacle in designing doubly efficient PAC‑verification protocols.