无记忆最佳选择问题
The Memoryless Best-Choice Problem
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中文总结 AI 辅助
研究在记忆约束下从已知连续分布选总体排名第一项目的无记忆最佳选择问题，利用平面泊松过程推导最优停止规则性质，与经典全信息模型比较，解析确定问题特征并高精度数值近似。
中文摘要 AI 辅助
从已知连续分布中采样的随机序列被观测，目标是选择总体排名第一的项目。被拒绝的项目不能被召回并立即从记忆中删除。在此记忆约束下，选择问题不适用于最优停止的递归方法，成为全局优化任务。我们关注具有无限多选择机会的重交通形式的问题，用平面泊松过程（PPP）表述。利用PPP的对称性推导最优停止规则的基本结构性质，包括边界方程的平衡和两个关键积分恒等式。始终与该问题的经典全信息对应物进行全面比较，回顾离散和连续时间模型。通过解析确定问题的最优值、停止规则和其他特征，并高精度数值近似。
英文摘要
A random sequence sampled from a known continuous distribution is observed with the objective to choose an item with the overall rank one. A rejected item cannot be recalled and is immediately erased from the memory. Under this memory constraint, the choice problem is not amenable to recursive methods of optimal stopping and becomes a global optimisation task. We focus on a heavy-traffic form of the problem with infinitely many choice opportunities, which we state in terms of a planar Poisson process (PPP). Symmetries of the PPP are used to derive basic structural properties of the optimal stopping rule, including the balance at the boundary equation, and two key integral identities. Throughout, we make throrough comparison to the classic full-information counterpart of the problem, revisiting both discrete- and continuous-time models. The optimal value, stopping rule and other characteristics of the problem are determined analytically and approximated numerically with high precision.
