The Diverse Cohort Selection Problem
This work addresses resource allocation in hiring and admissions for firms and universities, but it is incremental as it builds on existing combinatorial pure exploration methods.
The paper tackles the problem of selecting an optimal cohort of employees or students under budget constraints by generalizing a combinatorial pure exploration algorithm to handle varying costs and information levels of arm pulls, and demonstrates its application to university admissions with real data, showing comparable budget usage to current processes.
How should a firm allocate its limited interviewing resources to select the optimal cohort of new employees from a large set of job applicants? How should that firm allocate cheap but noisy resume screenings and expensive but in-depth in-person interviews? We view this problem through the lens of combinatorial pure exploration (CPE) in the multi-armed bandit setting, where a central learning agent performs costly exploration of a set of arms before selecting a final subset with some combinatorial structure. We generalize a recent CPE algorithm to the setting where arm pulls can have different costs and return different levels of information. We then prove theoretical upper bounds for a general class of arm-pulling strategies in this new setting. We apply our general algorithm to a real-world problem with combinatorial structure: incorporating diversity into university admissions. We take real data from admissions at one of the largest US-based computer science graduate programs and show that a simulation of our algorithm produces a cohort with hiring overall utility while spending comparable budget to the current admissions process at that university.