Title: Secretary type problems under the Mallows model

报告人：刘旭钧  西交利物浦大学

Abstract: The secretary problem is a well-known question in sequential analysis and optimal stopping theory which asks how to maximize the probability of finding the optimal applicant in a sequentially examined list and where accept/reject decisions are made in real-time. An extension of the classical secretary problem is the so-called “postdoc problem”, in which one is asked to devise a strategy that identifies the second-best applicant with highest possible probability of success. Another extension is the “dowry problem with multiple choices” (henceforth, the dowry problem). In this case, one is allowed to make $r \ge 2$ choices and is asked to find a strategy that can select the optimal applicant with largest possibility of success.

The Mallows distribution is a Gaussian-like distribution for permutations. It is widely used in the statistics and machine learning community for rankings and can model the increasing/decreasing trend in the quality of applicants. We use a combinatorial approach to solve the postdoc problem and the dowry problem for the untraditional setting where the applicants are not presented uniformly at random but rather according to permutations drawn from the Mallows distribution. Joint work with Olgica Milenkovic and George~Moustakides.

About the speaker: Liu Xujun, obtained his PhD from Math at UIUC, supervised by Prof. Kostochka. His research interest lies in the field of combinatorics, specifically coloring of graphs, Ramsey theory, and the application of combinatorics in other fields such as information theory and computer science. He currently works at Xi'an Jiaotong-Liverpool University.

时间：2021年11月17日（周三） 16:00-17:00

地点：腾讯会议 ID: 285 029 180

邀请人：孟宪昌 数学学院教授