A Unified Approach to Fair Online Learning via Blackwell Approachability

TL;DR

This paper introduces a unified framework for fair online learning using Blackwell approachability, addressing unknown context distributions and fairness constraints like demographic parity in a repeated game setting.

Contribution

It adapts Blackwell's approachability theory to handle unknown contexts and fairness constraints, providing necessary and sufficient conditions for fair learning objectives.

Findings

Characterizes when fairness constraints are compatible with learning objectives.

Provides a framework to identify optimal trade-offs when constraints are incompatible.

Applies the approach to group-wise no-regret, calibration, and demographic parity.

Abstract

We provide a setting and a general approach to fair online learning with stochastic sensitive and non-sensitive contexts. The setting is a repeated game between the Player and Nature, where at each stage both pick actions based on the contexts. Inspired by the notion of unawareness, we assume that the Player can only access the non-sensitive context before making a decision, while we discuss both cases of Nature accessing the sensitive contexts and Nature unaware of the sensitive contexts. Adapting Blackwell's approachability theory to handle the case of an unknown contexts' distribution, we provide a general necessary and sufficient condition for learning objectives to be compatible with some fairness constraints. This condition is instantiated on (group-wise) no-regret and (group-wise) calibration objectives, and on demographic parity as an additional constraint. When the objective is not compatible with the constraint, the provided framework permits to characterise the optimal trade-off between the two.