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 . 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.

中文翻译：

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在线平衡随机输入

我们认为在线量平衡游戏，向量v_牛逼，随机均匀地选择{ - 1，+ 1} ^ñ，到达时间和标志X_牛逼 ∈{ - 1，+ 1}必须立即抵达后回升v_牛逼。我们的目标是尽量减少大号^∞签署的总和的常态。我们给出了一种在线策略来高概率地选择具有值O（n ^1/2）的符号x _t。直到常量，即使向量是预先给出的，这也是最好的选择。