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Online Discrepancy Minimization via Persistent Self-Balancing Walks

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 نشر من قبل Tung Mai
 تاريخ النشر 2021
  مجال البحث الهندسة المعلوماتية
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We study the online discrepancy minimization problem for vectors in $mathbb{R}^d$ in the oblivious setting where an adversary is allowed fix the vectors $x_1, x_2, ldots, x_n$ in arbitrary order ahead of time. We give an algorithm that maintains $O(sqrt{log(nd/delta)})$ discrepancy with probability $1-delta$, matching the lower bound given in [Bansal et al. 2020] up to an $O(sqrt{log log n})$ factor in the high-probability regime. We also provide results for the weighted and multi-col



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