论文标题
通过通用赌博策略在有限随机过程的置信序列上
On Confidence Sequences for Bounded Random Processes via Universal Gambling Strategies
论文作者
论文摘要
本文考虑了构建置信序列的问题，该问题是一系列置信区间，随着时间的流逝，它们均匀地保持，用于估计有限的实重值随机过程的平均值。本文重新审视了从天然\ emph {两匹马种族}的观点中建立的基于赌博的方法，并展示了Cover（1991）的通用投资组合引起的结果算法的新属性。本文的主要结果是一种基于下限的混合物的新算法，该算法与Cover的通用投资组合的性能近似于恒定的每轮时间复杂性。在（Fan等，2015）中对对数函数的下限进行的高阶概括，该功能是针对该算法的关键技术开发的，它可能具有独立的兴趣。
This paper considers the problem of constructing a confidence sequence, which is a sequence of confidence intervals that hold uniformly over time, for estimating the mean of bounded real-valued random processes. This paper revisits the gambling-based approach established in the recent literature from a natural \emph{two-horse race} perspective, and demonstrates new properties of the resulting algorithm induced by Cover (1991)'s universal portfolio. The main result of this paper is a new algorithm based on a mixture of lower bounds, which closely approximates the performance of Cover's universal portfolio with constant per-round time complexity. A higher-order generalization of a lower bound on a logarithmic function in (Fan et al., 2015), which is developed as a key technique for the proposed algorithm, may be of independent interest.
