On-Line Balancing of Random Inputs

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We consider an online vector balancing game where vectors $v_t$, chosen uniformly at random ${-1,+1}^n$, arrive over time and a sign $x_t in {-1,+1}$ must be picked immediately upon the arrival of $v_t$. The goal is to minimize the $L^infty$ norm of the signed sum $sum_t x_t v_t$. We give an online strategy for picking the signs $x_t$ th...More