[Paper Review] Chasing Fairness Under Distribution Shift: A Model Weight Perturbation Approach

Zhimeng Jiang, Xiaotian Han+5 more|arXiv (Cornell University)|Mar 6, 2023

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TL;DR

This paper proposes Robust Fairness Regularization (RFR), a model weight perturbation approach that ensures fairness under distribution shift by enforcing robustness to worst-case weight perturbations within groups. The method achieves superior fairness-accuracy trade-offs on synthetic and real-world distribution shifts compared to baselines, grounded in a theoretical equivalence between distribution shift and model weight perturbation.

ABSTRACT

Fairness in machine learning has attracted increasing attention in recent years. The fairness methods improving algorithmic fairness for in-distribution data may not perform well under distribution shifts. In this paper, we first theoretically demonstrate the inherent connection between distribution shift, data perturbation, and model weight perturbation. Subsequently, we analyze the sufficient conditions to guarantee fairness (i.e., low demographic parity) for the target dataset, including fairness for the source dataset, and low prediction difference between the source and target datasets for each sensitive attribute group. Motivated by these sufficient conditions, we propose robust fairness regularization (RFR) by considering the worst case within the model weight perturbation ball for each sensitive attribute group. We evaluate the effectiveness of our proposed RFR algorithm on synthetic and real distribution shifts across various datasets. Experimental results demonstrate that RFR achieves better fairness-accuracy trade-off performance compared with several baselines. The source code is available at \url{https://github.com/zhimengj0326/RFR_NeurIPS23}.

Motivation & Objective

• To address the critical challenge of fairness degradation in machine learning models under distribution shift, especially in high-stakes applications like healthcare and criminal justice.
• To theoretically establish the equivalence between distribution shift, data perturbation, and model weight perturbation in terms of loss value.
• To identify sufficient conditions for fairness transferability from source to target distributions, emphasizing prediction difference across sensitive groups.
• To develop a robust fairness regularization (RFR) method that explicitly enforces fairness under worst-case model weight perturbations for each sensitive attribute group.
• To enable practical deployment of fair models in real-world settings where data distributions shift post-deployment.

Proposed method

• Theoretically proves that distribution shift is equivalent to model weight perturbation by showing loss equivalence under arbitrary model architectures and loss functions.
• Proposes RFR as a regularization technique that optimizes for the worst-case model weight perturbation within a ball for each sensitive group, ensuring robust fairness.
• Uses first-order Taylor expansion to approximate the inner maximization problem in RFR, enabling efficient computation via two forward and backward passes per update.
• Integrates the RFR loss into the training objective to jointly optimize for accuracy and fairness robustness under distribution shift.
• Employs a perturbation-based formulation that explicitly models the impact of distribution shift on fairness via model weight variations.
• Applies the method across diverse datasets with both synthetic and real-world distribution shifts to validate robustness.

Experimental results

Research questions

• RQ1 Can distribution shift be formally linked to model weight perturbation in terms of loss equivalence?
• RQ2 What sufficient conditions ensure fairness transferability from source to target distributions under distribution shift?
• RQ3 Can robust fairness be achieved by optimizing for worst-case model weight perturbations within each sensitive group?
• RQ4 How does the proposed RFR method compare to existing fairness baselines in terms of fairness-accuracy trade-off under distribution shift?
• RQ5 Does the RFR method maintain fairness performance across both synthetic and real-world distribution shifts?

Key findings

• The paper establishes a theoretical equivalence between distribution shift and model weight perturbation, showing that any distribution shift can be represented as a perturbation in model weights that preserves loss values.
• RFR achieves better fairness-accuracy trade-offs than multiple baselines across various datasets with both synthetic and real distribution shifts.
• The method effectively maintains low demographic parity disparity under distribution shift, even when the source model is already fair.
• Experiments show that hyperparameter λ enables effective control over the fairness-accuracy trade-off, with optimal performance achieved at moderate λ values.
• The first-order approximation of the inner maximization in RFR enables efficient training with only two forward and backward passes per update, making the method scalable.
• Empirical results confirm that prediction difference between source and target distributions for each sensitive group is a critical factor in fairness transferability.