Supervised fairness-aware machine learning under distribution shifts is an emerging field that addresses the challenge of maintaining equitable and unbiased predictions when faced with changes in data distributions from source to target domains. In real-world applications, machine learning models are often trained on a specific dataset but deployed in environments where the data distribution may shift over time due to various factors. This shift can lead to unfair predictions, disproportionately affecting certain groups characterized by sensitive attributes, such as race and gender. In this survey, we provide a summary of various types of distribution shifts and comprehensively investigate existing methods based on these shifts, highlighting six commonly used approaches in the literature. Additionally, this survey lists publicly available datasets and evaluation metrics for empirical studies. We further explore the interconnection with related research fields, discuss the significant challenges, and identify potential directions for future studies.

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