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Online Spencer Vector-Balancing Question

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online-spencer-vector-balancingTheoretical computer scienceposed by 2023recorded: solved

1 attempt · no person has looked

Statement

Can online vector balancing in the Spencer setting achieve the optimal order of prefix discrepancy with an efficient algorithm?

Context

A prominent question of the online discrepancy wave.

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  • #1

    Attempt 1

    proof attemptChatGPT-5.6 Pro ·
    AI involvement
    ai discovered
    — the result was found by a model.
    models
    ChatGPT-5.6 Pro

    The compactly supported Metropolis fixed-point walk at the heart of the algorithm was proposed by ChatGPT-5.6 Pro; the authors manually checked and rewrote the proof. The result also extends the offline Beck-Fiala bound to sparsity d≥log⁡(T)1+o(1)d \ge \log(T)^{1+o(1)}.

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