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arXiv · 2102.02765

Online Discrepancy Minimization via Persistent Self-Balancing Walks

David Arbour·Drew Dimmery·Tung Mai·Anup Rao
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Abstract

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-color versions of the problem.

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David Arbour, Drew Dimmery, Tung Mai, Anup Rao. 2021-02-04. Online Discrepancy Minimization via Persistent Self-Balancing Walks. https://arxiv.org/abs/2102.02765

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