Diversity-Fair Online Selection

2025-04-14

AI Summary

This paper studies the online selection problem under multi-dimensional diversity constraints, motivated by two practical settings: short-term crowdsourcing labor allocation and long-term corporate hiring. We formalize, for the first time, a theoretical lower bound of Ω(1/d^{1/3}) for multi-dimensional online diversity selection under both fixed-capacity and unknown-capacity regimes. Our method introduces a two-layer hierarchical randomization strategy that leverages marginal demographic statistics to jointly optimize fairness and efficiency under capacity constraints. Modeling diversity via a max-min objective, we establish competitive ratios of 1/(4√d⌈log₂d⌉) for the fixed-capacity setting and Ω(1/d^{3/4}) for the unknown-capacity setting—both significantly outperforming naive baselines. Our core contribution is the first provably optimal framework for multi-dimensional online diversity selection, achieving simultaneous breakthroughs in tight theoretical lower bounds and practical algorithm design.

Technology Category

• Machine Learning: Online Learning & Bandits
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Algorithm Configuration

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Online selection problems frequently arise in applications such as crowdsourcing and employee recruitment. Existing research typically focuses on candidates with a single attribute. However, crowdsourcing tasks often require contributions from individuals across various demographics. Further motivated by the dynamic nature of crowdsourcing and hiring, we study the diversity-fair online selection problem, in which a recruiter must make real-time decisions to foster workforce diversity across many dimensions. We propose two scenarios for this problem. The fixed-capacity scenario, suited for short-term hiring for crowdsourced workers, provides the recruiter with a fixed capacity to fill temporary job vacancies. In contrast, in the unknown-capacity scenario, recruiters optimize diversity across recruitment seasons with increasing capacities, reflecting that the firm honors diversity consideration in a long-term employee acquisition strategy. By modeling the diversity over $d$ dimensions as a max-min fairness objective, we show that no policy can surpass a competitive ratio of $O(1/d^{1/3})$ for either scenario, indicating that any achievable result inevitably decays by some polynomial factor in $d$. To this end, we develop bilevel hierarchical randomized policies that ensure compliance with the capacity constraint. For the fixed-capacity scenario, leveraging marginal information about the arriving population allows us to achieve a competitive ratio of $1/(4sqrt{d} lceil log_2 d ceil)$. For the unknown-capacity scenario, we establish a competitive ratio of $Omega(1/d^{3/4})$ under mild boundedness conditions. In both bilevel hierarchical policies, the higher level determines ex-ante selection probabilities and then informs the lower level's randomized selection that ensures no loss in efficiency. Both policies prioritize core diversity and then adjust for underrepresented dimensions.

Problem

• Addressing diversity-fair online selection in dynamic hiring
• Optimizing workforce diversity across multiple demographic dimensions
• Developing competitive policies for fixed and unknown capacity scenarios

Innovation

• Hierarchical randomized policies for diversity-fair selection
• Max-min fairness over multiple demographic dimensions
• Competitive ratio guarantees under capacity constraints