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The Yun-Sra-Jadbabaie SS-RS-GD Inequalities

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yun-sra-jadbabaie-shuffling-inequalitiesAlgorithms & optimizationposed by Chulhee Yun, Suvrit Sra, Ali Jadbabaie, 2021recorded: solved

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Statement

Yun, Sra and Jadbabaie posed as a COLT 2021 open question whether, for well-conditioned symmetric matrices, the operators encoding the expected iterate of single-shuffle SGD, random-reshuffle SGD and gradient descent on a quadratic finite sum satisfy ∥Wss∥≤∥Wrs∥≤∥Wgd∥\|W_{ss}\| \le \|W_{rs}\| \le \|W_{gd}\|. They do.

Context

A COLT open question about why shuffling beats sampling in SGD, a question the optimization community has tracked since 2021.

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  • #1

    Attempt 1

    proof attemptGPT-5.5 Pro (extended) with Binghui Peng ·
    AI involvement
    ai discovered
    — the result was found by a model.
    models
    GPT-5.5 Pro (extended)
    people
    Binghui Peng

    The paper states the proof was found via GPT-5.5 Pro prompted by the author, and a footnote says the proof idea was completely generated by the model, linking the shared conversation. The write-up was assembled by the author.

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