Optimal Multiple Stopping Rule for Warm-Starting Sequential Selection

The Warm-starting Sequential Selection Problem and its Multi-round Extension

In the Sequential Selection Problem (SSP), immediate and irrevocable decisions need to be made as candidates randomly arrive for a job interview. Standard SSP variants, such as the well-known secretary problem, begin with an empty selection set (cold-start) and perform the selection process once over a single candidate set (single-round). In this paper we address these two limitations. First, we introduce the novel Warm-starting SSP (WSSP) setting which considers at hand a reference set, a set of previously selected items of a given quality, and tries to update optimally that set by (re-)assig…

Sequential Resource Allocation with Positional Costs

We consider the problem of minimizing the total cost to run a sequence of $n$ tasks in the given order by $k$ agents under the positional cost model. The cost to run a task not only depends on the intrinsic cost of the task itself, but also monotonically related to the position this task is in the working list of the agent assigned. Such a positional effect can naturally arise from the classic sum-of-completion-time minimization problems, and is also well motivated by the varying efficiency when an agent works in reality (such as due to the learning effects or deteriorating effects). Also, it …

对称伯努利假设下序贯概率比检验最优性的一个简单几何证明

A Simple Geometric Proof of the Optimality of the Sequential Probability Ratio Test for Symmetric Bernoulli Hypotheses

本文针对加权硬币偏差检验问题，通过将策略建模为二维整数格上的有偏随机游走，采用贪心局部扰动方法，给出了SPRT最优性的离散自包含几何证明。

带随机查询的秘书问题的最优停止方法

Optimal Stopping Methodology for the Secretary Problem with Random Queries

本文研究允许向可能出错的专家进行随机查询的秘书问题变体，利用最优停止理论优化查询时刻并设计终止决策机制，以最大化选中最佳候选人的概率。