Closing the Gap: Group-Aware Parallelization for the Secretary Problem with Biased Utilities

39 Pages Posted: 3 Sep 2019 Last revised: 5 Mar 2020

See all articles by Jad Salem

Jad Salem

Georgia Institute of Technology

Swati Gupta

Georgia Institute of Technology

Date Written: August 27, 2019

Abstract

The secretary problem and its variants select candidates in an online setting while assuming access to their true rankings (or utilities) as they arrive. Motivated by the existence of implicit bias in evaluations of candidates from different demographic groups (e.g., gender, age, race), we consider the biased secretary problem, where instead of observing the true utility $w(e)$ of each candidate $e$, the algorithm only observes a biased estimate $\tilde{w}(e)$. The true utilities of the candidates are observed only after the entire sequence of candidates has been revealed. The goal is to be competitive with respect to an offline oracle that knows true utilities.

We first assume that the bias factors are group-dependent (e.g., dependent on race, age, gender, nationality): for each candidate $e$ in group $G_i$, the observed utility is $\tilde{w}(e) = w(e)/\beta_i$. We posit that a desirable and fair property for selection of candidates is ranked demographic parity: for any $p$, the probability of selecting a candidate in the top $p$th percentile in any group is similar across demographic groups of equal size. We show that group-agnostic methods can be suboptimal both in terms of fairness and utility, and propose group-aware parallelization, \textsc{Gap}, as an effective tool to get provably competitive algorithms. We show that \textsc{Gap} can be tweaked for fairly general stochastic and adversarial settings by adapting techniques in the secretary problem literature. We then propose a more individualized model of bias, where due to implicit bias and limitations of testing, the algorithm only observes an interval $[\ell_e,u_e]$ containing the true utility of candidate $e$. In this setting, we only have pair-wise comparisons between candidates when their observed intervals do not overlap. We then provide an algorithm for this setting which is order-optimal and it extends to the case when elements can only be compared with respect to a partial order.

Keywords: secretary problem, bias, online selection, partial order

Suggested Citation

Salem, Jad and Gupta, Swati, Closing the Gap: Group-Aware Parallelization for the Secretary Problem with Biased Utilities (August 27, 2019). Available at SSRN: https://ssrn.com/abstract=3444283 or http://dx.doi.org/10.2139/ssrn.3444283

Jad Salem

Georgia Institute of Technology ( email )

Atlanta, GA 30332
United States

Swati Gupta (Contact Author)

Georgia Institute of Technology ( email )

Atlanta, GA 30332
United States

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