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Fair Secretaries with Unfair Predictions

Eric Balkanski, Will Ma, Andreas Maggiori

TL;DR

This work addresses fairness when using potentially biased predictions in the secretary problem by introducing the pegging family of algorithms. It achieves strong value guarantees that degrade gracefully with prediction error while guaranteeing a constant probability of hiring the true best candidate, addressing unfairness in prior learning-augmented approaches. The framework extends to the $k$-secretary setting with provable smoothness and per-candidate fairness, supported by experiments that demonstrate robust performance across diverse prediction quality and bias scenarios. The pegging approach offers a unified, simpler analysis and broad applicability to prediction-driven online selection problems.

Abstract

Algorithms with predictions is a recent framework for decision-making under uncertainty that leverages the power of machine-learned predictions without making any assumption about their quality. The goal in this framework is for algorithms to achieve an improved performance when the predictions are accurate while maintaining acceptable guarantees when the predictions are erroneous. A serious concern with algorithms that use predictions is that these predictions can be biased and, as a result, cause the algorithm to make decisions that are deemed unfair. We show that this concern manifests itself in the classical secretary problem in the learning-augmented setting -- the state-of-the-art algorithm can have zero probability of accepting the best candidate, which we deem unfair, despite promising to accept a candidate whose expected value is at least $\max\{Ω(1) , 1 - O(ε)\}$ times the optimal value, where $ε$ is the prediction error. We show how to preserve this promise while also guaranteeing to accept the best candidate with probability $Ω(1)$. Our algorithm and analysis are based on a new "pegging" idea that diverges from existing works and simplifies/unifies some of their results. Finally, we extend to the $k$-secretary problem and complement our theoretical analysis with experiments.

Fair Secretaries with Unfair Predictions

TL;DR

This work addresses fairness when using potentially biased predictions in the secretary problem by introducing the pegging family of algorithms. It achieves strong value guarantees that degrade gracefully with prediction error while guaranteeing a constant probability of hiring the true best candidate, addressing unfairness in prior learning-augmented approaches. The framework extends to the -secretary setting with provable smoothness and per-candidate fairness, supported by experiments that demonstrate robust performance across diverse prediction quality and bias scenarios. The pegging approach offers a unified, simpler analysis and broad applicability to prediction-driven online selection problems.

Abstract

Algorithms with predictions is a recent framework for decision-making under uncertainty that leverages the power of machine-learned predictions without making any assumption about their quality. The goal in this framework is for algorithms to achieve an improved performance when the predictions are accurate while maintaining acceptable guarantees when the predictions are erroneous. A serious concern with algorithms that use predictions is that these predictions can be biased and, as a result, cause the algorithm to make decisions that are deemed unfair. We show that this concern manifests itself in the classical secretary problem in the learning-augmented setting -- the state-of-the-art algorithm can have zero probability of accepting the best candidate, which we deem unfair, despite promising to accept a candidate whose expected value is at least times the optimal value, where is the prediction error. We show how to preserve this promise while also guaranteeing to accept the best candidate with probability . Our algorithm and analysis are based on a new "pegging" idea that diverges from existing works and simplifies/unifies some of their results. Finally, we extend to the -secretary problem and complement our theoretical analysis with experiments.

Paper Structure

This paper contains 11 sections, 11 theorems, 49 equations, 1 figure, 5 algorithms.

Table of Contents

  1. Introduction
  2. Related work
  3. Preliminaries
  4. Algorithm and Analysis
  5. Extension: $k$-Secretary problem with predictions
  6. Experiments
  7. Limitations and Future Work
  8. Additional discussion and missing analysis for single secretary
  9. Unfair outcomes in previous work
  10. The Pegging algorithm
  11. Missing analysis for the k-secretary pegging algorithm

Key Result

Lemma 1

Additive-Pegging satisfies $u_{\mathcal{A}} \ \geq u_{i^*} - 4 \mathop{\mathrm{\varepsilon}}\nolimits (\mathcal{I}) , \; \forall \mathcal{I}$ with probability 1.

Figures (1)

  • Figure 1: Competitive ratio and fairness of different algorithms, for each instance type and level of $\mathop{\mathrm{\varepsilon}}\nolimits$.

Theorems & Definitions (19)

  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Theorem 3
  • Theorem 4
  • Theorem 5
  • Theorem 6
  • proof
  • Theorem 6
  • ...and 9 more