Online Discrepancy Minimization via Persistent Self-Balancing Walks

02/04/2021

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by   David Arbour, et al.

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We study the online discrepancy minimization problem for vectors in ℝ^d in the oblivious setting where an adversary is allowed fix the vectors x_1, x_2, …, x_n in arbitrary order ahead of time. We give an algorithm that maintains O(√(log(nd/δ))) discrepancy with probability 1-δ, matching the lower bound given in [Bansal et al. 2020] up to an O(√(loglog n)) factor in the high-probability regime. We also provide results for the weighted and multi-color versions of the problem.