Rashomon Sets and Model Multiplicity in Federated Learning

TL;DR

This paper extends the concept of Rashomon sets to federated learning, providing formal definitions, estimation methods, and an empirical study to understand model multiplicity and improve fairness in decentralized settings.

Contribution

It introduces the first formalization of Rashomon sets in federated learning, including three perspectives, estimation techniques, and a multiplicity-aware training pipeline.

Findings

All three Rashomon set definitions provide valuable insights into model diversity.

The proposed methods enable better alignment of models with local data and fairness.

Empirical results demonstrate the effectiveness of the federated Rashomon framework.

Abstract

The Rashomon set captures the collection of models that achieve near-identical empirical performance yet may differ substantially in their decision boundaries. Understanding the differences among these models, i.e., their multiplicity, is recognized as a crucial step toward model transparency, fairness, and robustness, as it reveals decision boundaries instabilities that standard metrics obscure. However, the existing definitions of Rashomon set and multiplicity metrics assume centralized learning and do not extend naturally to decentralized, multi-party settings like Federated Learning (FL). In FL, multiple clients collaboratively train models under a central server's coordination without sharing raw data, which preserves privacy but introduces challenges from heterogeneous client data distribution and communication constraints. In this setting, the choice of a single best model may homogenize predictive behavior across diverse clients, amplify biases, or undermine fairness guarantees. In this work, we provide the first formalization of Rashomon sets in FL.First, we adapt the Rashomon set definition to FL, distinguishing among three perspectives: (I) a global Rashomon set defined over aggregated statistics across all clients, (II) a t-agreement Rashomon set representing the intersection of local Rashomon sets across a fraction t of clients, and (III) individual Rashomon sets specific to each client's local distribution.Second, we show how standard multiplicity metrics can be estimated under FL's privacy constraints. Finally, we introduce a multiplicity-aware FL pipeline and conduct an empirical study on standard FL benchmark datasets. Our results demonstrate that all three proposed federated Rashomon set definitions offer valuable insights, enabling clients to deploy models that better align with their local data, fairness considerations, and practical requirements.