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 in {-1,+1}^n, arrive over time and a sign x_t ∈{-1,+1} must be picked immediately upon the arrival of v_t. The goal is to minimize the L^∞ norm of the signed sum ∑_t x_t v_t. We give an online strategy for picking the signs x_t that has value O(n^1/2) with high probability. Up to constants, this is the best possible even when the vectors are given in advance.
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