In learning-augmented online algorithms, predictions are usually valued for what they say: a value estimate, a solution, or an algorithmic recommendation. This paper shows that predictions can also be valuable solely due to their arrival time. We study the fundamental secretary problem augmented with a stochastic precursor: a content-free signal that is guaranteed to arrive no later than the best item, but is otherwise stochastically timed. The signal does not carry any additional information; nevertheless, its timing alone changes the structure of optimal stopping. We characterize optimal policies in the random-order and adversarial-order models. In random order, a single uniformly timed precursor already gives success probability at least $\frac12$, improving on the classic $\frac1e$ benchmark. With increasingly late precursors, the success probability approaches $1$. In adversarial order, for which traditional models do not admit strong guarantees, sufficiently concentrated precursors recover constant success guarantees. Our results show that such novel forms of asynchronous temporal information are a distinct and powerful form of advice in online decision making and may also be effective for other problems.

翻译：在学习增强型在线算法中，预测通常因其内容而受到重视：估值、解决方案或算法建议。本文表明，预测仅凭其到达时间也具有价值。我们研究了经典秘书问题的一个变体，该问题增加了一个随机前兆：一个无内容信号，保证不迟于最优项目到达，但其到达时间随机。该信号不携带任何附加信息；然而，仅凭其时间就能改变最优停止的结构。我们在随机顺序和对抗顺序模型下刻画了最优策略。在随机顺序中，单个均匀分布的前兆已能给出至少$\frac12$的成功概率，优于经典的$\frac1e$基准。随着前兆越来越晚，成功概率趋近于$1$。在对抗顺序中，传统模型无法提供强保证，而足够集中的前兆能恢复常数的成功保证。我们的结果表明，这种新颖的异步时间信息形式是在线决策中一种独特且强大的建议形式，也可能对其他问题有效。