Efficient UCB-Based Assignment Algorithm Under Unknown Utility with Application in Mentor-Mentee Matching

Shi, Yuyang; Mei, Yajun

doi:10.6339/24-JDS1151

Journal of Data Science

Efficient UCB-Based Assignment Algorithm Under Unknown Utility with Application in Mentor-Mentee Matching

Yuyang Shi ^† Yajun Mei

https://doi.org/10.6339/24-JDS1151

Pub. online: 24 September 2024 Type: Statistical Data Science

Open Access

^† This paper is part of the first author’s PhD dissertation at Georgia Institute of Technology.

Received
18 June 2024

Accepted
22 August 2024

Published
24 September 2024

Abstract

The assignment problem, crucial in various real-world applications, involves optimizing the allocation of agents to tasks for maximum utility. While it has been well-studied in the optimization literature when the underlying utilities between all agent-task pairs are known, research is sparse when the utilities are unknown and need to be learned from data on the fly. This paper addresses this gap, as motivated by mentor-mentee matching programs at many U.S. universities. We develop an efficient sequential assignment algorithm, with the aim of nearly maximizing the overall utility simultaneously over different time periods. Our proposed algorithm is to use stochastic bandit feedback to adaptively estimate the unknown utilities through linear regression models, integrating the Upper Confidence Bound (UCB) algorithm in the multi-armed bandit problem with the Hungarian algorithm in the assignment problem. We provide theoretical bounds of our algorithm for both the estimation error and the total regret. Additionally, numerical studies are also conducted to demonstrate the practical effectiveness of our algorithm.

Supplementary material

Supplementary Material

The supplementary materials online includes: Proofs of Lemmas and Theorems used in the paper, and Python code needed to reproduce the results.

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2024 The Author(s). Published by the School of Statistics and the Center for Applied Statistics, Renmin University of China.

Open access article under the CC BY license.

Keywords

bandits estimation optimal assignment upper confidence bound

Funding

This research was supported in part by NSF grant DMS-2015405 and by the National Center for Advancing Translational Sciences of the National Institutes of Health under Award Number UL1TR002378. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.

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