AI 中文总结
研究身份真实的在线决策问题，引入新限制定义身份真实性差距，设计算法确定其大于0.5且有0.81上限，还研究了该算法与定价机制关系，发现身份真实性会打破在线算法与定价的常规联系。
AI 中文摘要
在贝叶斯在线选择中，决策者观察一系列随机奖励，并必须立即且不可撤销地接受或拒绝每个实现的值。奖励来自已知分布，即其身份。经典先知不等式将在线算法与离线最优进行比较，而近期工作研究相对于知道身份到达顺序的最优在线算法的信息差距。我们引入了由与身份无关的决策驱动的新限制：决策者观察当前值，但仅在决定是否接受后才了解其身份，我们称此类算法为身份真实的。我们定义身份真实性差距为身份真实算法相对于最优在线基准可实现的最优最坏情况近似。此差距介于顺序竞争比率和身份盲目性差距之间。我们设计了一种算法，确定身份真实性差距严格大于0.5，从而将其与恰好为0.5的身份盲目性差距区分开来。我们用身份真实性差距的0.81上限补充这一结果，该上限严格低于顺序竞争比率的已知上限0.829。最后，我们研究身份真实算法与定价机制之间的关系。受先知不等式中张贴价格的力量问题的启发，我们表明身份真实性打破了在线算法与定价之间的通常联系：存在一个实例，对于该实例，最优身份真实算法不能由任何定价机制实现。
英文摘要
In Bayesian online selection, a decision-maker observes a sequence of stochastic rewards and must immediately and irrevocably accept or reject each realized value. The rewards come from known distributions, referred to as their identities. Whereas classical prophet inequalities compare online algorithms to the offline optimum, recent work studies information gaps relative to the optimal online algorithm, which knows the identities' arrival order. We introduce a new restriction motivated by identity-independent decision-making: the decision-maker observes the current value but learns its identity only after deciding whether to accept it. We call such algorithms identity-truthful. We define the identity-truthfulness gap as the optimal worst-case approximation achievable by identity-truthful algorithms relative to the optimal online benchmark. This gap lies between the order-competitive ratio [Ezra et al. 2023] and the identity-blindness gap [Ezra et al. 2024]. We design an algorithm establishing that the identity-truthfulness gap is strictly greater than $0.5$, thereby separating it from the identity-blindness gap, which is exactly $0.5$. We complement this result with an upper bound of $0.81$ on the identity-truthfulness gap, which is strictly lower than the known upper bound of $0.829$ on the order-competitive ratio [Chen et al. 2024]. Finally, we study the relationship between identity-truthful algorithms and pricing mechanisms. Motivated by questions on the power of posted prices in prophet inequalities [Duetting et al. 2020], we show that identity-truthfulness breaks the usual connection between online algorithms and pricing: there exists an instance for which the optimal identity-truthful algorithm cannot be implemented by any pricing mechanism.
