Closing the Oracle-Complexity Gap in Derivative-Free Convex Optimization: A Near-Quadratic Lower Bound from Exact Function Values · HackerPapers discussions

Closing the Oracle-Complexity Gap in Derivative-Free Convex Optimization: A Near-Quadratic Lower Bound from Exact Function Values — mentioned by blt

Tue, 06 Oct 2026 04:05:12 GMT

Every few years, a derivative-free neural network optimization algorithm gets some hype. I'd bet my life savings that none of them ever make an impact. Derivative-free optimization can be useful for genuinely discontinuous objectives [1], but common neural network objectives are smooth and/or Lipschitz. The gradient is useful. Instead of trying random directions and hoping that one of them is an improvement, it tells you where to go. The more parameters you have, the more useful it becomes. A strict complexity gap between gradient-based and derivative-free Lipschitz convex optimization has…

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Closing the Oracle-Complexity Gap in Derivative-Free Convex Optimization: A Near-Quadratic Lower Bound from Exact Function Values — mentioned by varenc

Sat, 18 Jul 2026 18:14:12 GMT

Digression: You can link directly to a page in a pdf with a url like this: https://arxiv.org/pdf/2607.13335#page=27

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Closing the Oracle-Complexity Gap in Derivative-Free Convex Optimization: A Near-Quadratic Lower Bound from Exact Function Values — mentioned by applfanboysbgon

Sat, 18 Jul 2026 13:38:19 GMT

Two points: - Hasn't been peer reviewed yet, so take with a grain of salt. This applies to all claimed proofs, not just AI-generated ones. Even humans hallucinate proofs too! - The prompt is on page 27 here[1]. It is ten pages of advanced mathematics priming the model in the right direction, apparently informed by a year of prior research. That doesn't invalidate the result if it is genuine, but it is worth noting that this wasn't a matter of "ChatGPT, solve this unsolved problem. Make no mistakes." and required substantial domain expertise and human research beforehand.…

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