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Machine learning systems based on minimizing average error have been shown toperform inconsistently across notable subsets of the data, which is not exposedby a low average error for the entire dataset. In consequential social andeconomic applications, where data represent people, this can lead todiscrimination of underrepresented gender and ethnic groups. Given theimportance of bias mitigation in machine learning, the topic leads tocontentious debates on how to ensure fairness in practice (data bias versusalgorithmic bias). Distributionally Robust Optimization (DRO) seeminglyaddresses this problem by minimizing the worst expected risk acrosssubpopulations. We establish theoretical results that clarify the relationbetween DRO and the optimization of the same loss averaged on an adequatelyweighted training dataset. The results cover finite and infinite number oftraining distributions, as well as convex and non-convex loss functions. Weshow that neither DRO nor curating the training set should be construed as acomplete solution for bias mitigation: in the same way that there is nouniversally robust training set, there is no universal way to setup a DROproblem and ensure a socially acceptable set of results. We then leverage theseinsights to provide a mininal set of practical recommendations for addressingbias with DRO. Finally, we discuss ramifications of our results in otherrelated applications of DRO, using an example of adversarial robustness. Ourresults show that there is merit to both the algorithm-focused and thedata-focused side of the bias debate, as long as arguments in favor of thesepositions are precisely qualified and backed by relevant mathematics knowntoday.

Algorithmic Bias and Data Bias: Understanding the Relation between Distributionally Robust Optimization and Data Curation