The last success problem is an optimal stopping problem that aims to maximize the probability of stopping on the last success in a sequence of independent $n$ Bernoulli trials. In the classical setting where complete information about the distributions is available, Bruss~\cite{B00} provided an optimal stopping policy that ensures a winning probability of $1/e$. However, assuming complete knowledge of the distributions is unrealistic in many practical applications. This paper investigates a variant of the last success problem where samples from each distribution are available instead of complete knowledge of them. When a single sample from each distribution is allowed, we provide a deterministic policy that guarantees a winning probability of $1/4$. This is best possible by the upper bound provided by Nuti and Vondr\'{a}k~\cite{NV23}. Furthermore, for any positive constant $\epsilon$, we show that a constant number of samples from each distribution is sufficient to guarantee a winning probability of $1/e-\epsilon$.

翻译：末次成功问题是一个最优停止问题，其目标是在一系列独立的$n$次伯努利试验中，最大化在最后一次成功时停止的概率。在能够获得分布完整信息的经典设定下，Bruss~\cite{B00}提出了一种最优停止策略，该策略能确保$1/e$的获胜概率。然而，在许多实际应用中，假设完全掌握分布信息是不现实的。本文研究末次成功问题的一个变体，其中仅可获得每个分布的样本而非其完整信息。当允许从每个分布中抽取单个样本时，我们提出了一种确定性策略，该策略可保证$1/4$的获胜概率。根据Nuti和Vondr\'{a}k~\cite{NV23}提供的上界，该结果已达到最优。此外，对于任意正常数$\epsilon$，我们证明从每个分布中获取常数个样本足以保证$1/e-\epsilon$的获胜概率。