Confidence sequences are sequences of confidence sets that adapt to incoming data while maintaining validity. Recent advances have introduced an algorithmic formulation for constructing some of the tightest confidence sequences for bounded real random variables. These approaches use a coin-betting framework, where a player sequentially bets on differences between potential mean values and observed data. This letter establishes that such coin-betting formulation is optimal among all possible algorithmic frameworks for constructing confidence sequences that build on e-variables and sequential hypothesis testing.

翻译：置信序列是一系列随数据动态调整同时保持有效性的置信区间集合。近期研究进展提出了一种算法框架，用于为有界实随机变量构建最紧致的置信序列。该方法采用投币博弈框架，博弈者根据潜在均值与观测数据之间的差异进行序贯投注。本文证明，在基于e变量与序贯假设检验构建置信序列的所有可能算法框架中，此类投币博弈框架具有最优性。