FAIR FEDERATED LEARNING VIA BOUNDED GROUP LOSS

Abstract

Fair prediction across protected groups is an important constraint for many federated learning applications. However, prior work studying group fair federated learning lacks formal convergence or fairness guarantees. In this work we propose a general framework for provably fair federated learning. In particular, we explore and extend the notion of Bounded Group Loss as a theoretically-grounded approach for group fairness. Using this setup, we propose a scalable federated optimization method that optimizes the empirical risk under a number of group fairness constraints. We provide convergence guarantees for the method as well as fairness guarantees for the resulting solution. Empirically, we evaluate our method across common benchmarks from fair ML and federated learning, showing that it can provide both fairer and more accurate predictions than baseline approaches.

1. INTRODUCTION

Group fairness aims to mitigate unfair biases against certain protected demographic groups (e.g. race, gender, age) in the use of machine learning. Many methods have been proposed to incorporate group fairness constraints in centralized settings (e.g., Agarwal et al., 2018; Feldman et al., 2015; Hardt et al., 2016; Zafar et al., 2017a) . However, there is a lack of work studying these approaches in the context of federated learning (FL), a training paradigm where a model is fit to data generated by a set of disparate data silos, such as a network of remote devices or collection of organizations (Kairouz et al., 2019; Li et al., 2020; McMahan et al., 2017) . Mirroring concerns around fairness in non-federated settings, many FL applications similarly require performing fair prediction across protected groups. Unfortunately, as we show in Figure 1 , naively applying existing approaches to each client in a federated network in isolation may be inaccurate due to heterogeneity across clients-failing to produce a fair model across the entire population (Zeng et al., 2021) . Several recent works have considered addressing this issue by exploring specific forms of group fairness in FL (e.g., Chu et al., 2021; Cui et al., 2021; Du et al., 2021; Papadaki et al., 2022; Rodríguez-Gálvez et al., 2021; Zeng et al., 2021) . Despite promising empirical performance, these prior works lack formal guarantees surrounding the resulting fairness of the solutions (Section 2), which is problematic as it is unclear how the methods may perform in real-world FL deployments. In this work we provide a formulation and method for group fair FL that can provably satisfy global fairness constraints. Common group fairness notions that aim to achieve equal prediction quality between any two protected groups (e.g., Demographic Parity, Equal Opportunity (Hardt et al., 2016) ) are difficult to provably satisfy while simultaneously finding a model with high utility. Instead, we consider a different fairness notion known as Bounded Group Loss (BGL) (Agarwal et al., 2019) , which aims to promote worst group's performance, to capture these common group fairness criteria. As we show, a benefit of this approach is that in addition to 1



Figure 1: Naively applying fair learning method locally at each client might be problematic. Left: Due to data heterogeneity in FL, data distributions conditioned on each protected attribute (shown in different colors) may differ across clients. Fair FL aims to learn a model that provides fair prediction on the entire data distribution. Right: Empirical results (ACS dataset) verify that training with local fairness constraints alone induces higher error and worse fairness than using a global fairness constraint.

