  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.
