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Bounded Oracle Error in Nonconvex Stochastic Optimization

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bounded-oracle-noise-nonconvex-lower-boundAlgorithms & optimizationposed by Yossi Arjevani, Yair Carmon, John C. Duchi, Dylan J. Foster, Nathan Srebro, Blake Woodworth, 2023recorded: solved

1 attempt · no person has looked

Statement

Arjevani et al. asked whether almost-surely bounded oracle error permits a better rate than bounded variance for smooth nonconvex stochastic optimization. It does not: every randomized adaptive algorithm still needs Omega(dL/eps^2 + dL sigma^2/eps^4) queries, matching the standard upper bound.

Context

A question posed explicitly in a well-cited lower-bounds paper, familiar to the optimization-theory community but recent and specialist.

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  • #1

    Attempt 1

    proof attemptGPT-5.6 Sol with Jikai Jin ·
    AI involvement
    ai discovered
    — the result was found by a model.
    models
    GPT-5.6 Sol
    people
    Jikai Jin

    Stated in the abstract itself, not buried in an acknowledgment: "The proof was independently generated with GPT-5.6 Sol in Codex's Ultra mode during a two-hour session. The human author supplied the prompt and was responsible only for checking the proof and revising and polishing the manuscript."

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