What was already known
Stochastic gradient methods attain this rate. Earlier matching lower bounds assumed bounded variance but used an oracle without a uniform almost-sure error bound.
AI involvement
Jikai Jin says GPT-5.6 Sol independently generated the proof after he supplied the prompt. Jin checked and revised the model-generated argument; no human explanation of its sign-vector mechanism is documented.
The paper expressly says the model independently generated the proof after the human supplied the prompt; checking and manuscript polishing came later.
Importance
Closes the minimax-rate gap for the stated one-sample bounded-error oracle model.
Limitations
The oracle need not be a gradient of a sample loss and may be discontinuous in the query point. Conservative, finite-sum, samplewise-smooth and shared-sample variants are outside the theorem.
Technical verification
The named human author reports checking the proof of the stated lower bound, not merely accepting responsibility for it. This is a source-reported complete author check; no independent reviewer or machine formalization is documented and the review was not reproduced here.
Formal checking
Human proof check followed by manuscript revision
- Checker
- Jikai Jin, author
- Scope
- The model-generated proof of the K=1 fixed-law uniformly bounded-gradient-noise lower bound in Theorem 4.1
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Jin reports checking and polishing the proof, but the source does not attribute a human explanation of the sign encoding, KL accounting and escape-control mechanism. Few is the evidence default, not a finding that Jin lacks understanding.
Correction and publication history
Closes the minimax-rate gap for the stated one-sample bounded-error oracle model.
Read this published revision