In this paper we study the problem of tracking the mean of a piecewise stationary sequence of independent random variables. First we consider the case where the transition times are known and show that a direct running average performs the tracking in short time and with high accuracy. We then use a single valued weighted running average with a tunable parameter for the case when transition times are unknown and establish deviation bounds for the tracking accuracy. Our result has applications in choosing the optimal rewards for the multiarmed bandit scenario.

中文翻译：

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跟踪分段平稳序列的均值

在本文中，我们研究跟踪独立随机变量的分段平稳序列均值的问题。首先，我们考虑过渡时间已知的情况，并表明直接运行平均值可以在短时间内以高精度执行跟踪。然后，我们在过渡时间未知的情况下使用具有可调参数的单值加权运行平均值，并建立跟踪精度的偏差范围。我们的结果可应用于为多臂强盗场景选择最佳奖励。