Fair Secretaries with Unfair Predictions

2024-11-15

arXiv.org

AI Summary

This paper addresses fairness degradation in learning-augmented secretary problems caused by prediction bias—specifically, existing algorithms may select the optimal candidate with zero probability, violating decisional fairness. To resolve this, we propose a novel “threshold-pegging” mechanism: it dynamically anchors the selection threshold to predictions, ensuring the optimal candidate is selected with Ω(1) probability while preserving the original 1−O(ε) competitive ratio. Our approach unifies online algorithm design, probabilistic analysis, and learning-augmented frameworks, and naturally extends to the k-secretary problem. We provide rigorous theoretical guarantees and empirical validation: across diverse prediction error regimes, our method consistently outperforms baselines, achieving a synergistic balance between prediction-driven performance gains and provable fairness assurance.

Technology Category

• Search and Optimization: Learning to Search
• Machine Learning: Online Learning & Bandits
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• 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
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments

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 $max{Omega (1) , 1 - O(epsilon)}$ times the optimal value, where $epsilon$ is the prediction error. We show how to preserve this promise while also guaranteeing to accept the best candidate with probability $Omega(1)$. 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.

Problem

• Bias Mitigation
• Algorithmic Fairness
• Secretary Problem

Innovation

• Pegging
• Fairness
• Secretary Problem