On preserving non-discrimination when combining expert advice

TL;DR

This paper investigates how to combine non-discriminatory predictors in online decision making, revealing limitations for equalized odds and proposing solutions for equalized error rates.

Contribution

It demonstrates the impossibility of preserving equalized odds in online learning and offers a method for equalized error rates using multiplicative weights.

Findings

Equalized odds cannot be preserved when combining predictors online.

Running separate multiplicative weights for each group achieves equalized error rates.

Stronger algorithms than multiplicative weights cannot guarantee non-discrimination.

Abstract

We study the interplay between sequential decision making and avoiding discrimination against protected groups, when examples arrive online and do not follow distributional assumptions. We consider the most basic extension of classical online learning: "Given a class of predictors that are individually non-discriminatory with respect to a particular metric, how can we combine them to perform as well as the best predictor, while preserving non-discrimination?" Surprisingly we show that this task is unachievable for the prevalent notion of "equalized odds" that requires equal false negative rates and equal false positive rates across groups. On the positive side, for another notion of non-discrimination, "equalized error rates", we show that running separate instances of the classical multiplicative weights algorithm for each group achieves this guarantee. Interestingly, even for this notion, we show that algorithms with stronger performance guarantees than multiplicative weights cannot preserve non-discrimination.