Diversity-Fair Online Selection

TL;DR

The paper tackles online diversity-aware selection where a recruiter must maximize the minimum, dimension-weighted utility across $d$ diversity attributes under adversarial candidate arrivals. It introduces a bilevel randomized framework: a higher level outputs ex-ante selection probabilities guided by a fluid LP benchmark, while a lower level implements online dependent rounding to meet capacity constraints with no loss in objective value. Two scenarios are analyzed: a fixed-capacity setting with marginal information, achieving a competitive ratio of $1/(4\sqrt{d}\lceil\log_2 d\rceil)$, and an unknown-capacity setting with increasing capacity per round, achieving $\Omega(1/d^{3/4})$ under mild boundedness assumptions. An overarching impossibility barrier of $O(1/d^{1/3})$ is established, highlighting the polynomial degradation with $d$ for any policy, which motivates the proposed structured bilevel approaches. The results provide guidance for dynamically arriving candidates in crowdsourcing and long-horizon hiring while prioritizing core diversity and compensating underrepresented dimensions, with implications for fairness-aware online allocation in practice.

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 $1/(4\sqrt{d} \lceil \log_2 d \rceil)$. For the unknown-capacity scenario, we establish a competitive ratio of $Ω(1/d^{3/4})$ 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.

Figures (3)

• Figure 1: The Relationships among FC, UC, UFC, UUC, and FCS scenarios.
• Figure 2: Bilevel Solution Approach.
• Figure EC.1: Hard Instances for FHC Scenario.

Theorems & Definitions (15)

• Remark 1
• Proposition 1: Equivalence on the optimal Offline algorithm
• Remark 2
• Definition 1
• Proposition 2
• Theorem 1
• Proposition 3
• Lemma 1
• Lemma 2
• Lemma 3