Fair distributed machine learning with imbalanced data as a Stackelberg evolutionary game

Abstract Decentralised machine learning systems trained on heterogeneous and imbalanced data face a fundamental tension between predictive performance and equitable contribution across participating nodes. Here, we introduce two contribution-weighting mechanisms inspired by the principles of Stackelberg evolutionary games: the Deterministic Stackelberg Weighting Model (DSWM) and the Adaptive Stackelberg Weighting Model (ASWM), which dynamically regulate each node’s influence on the global model during training. We evaluate both methods in Single-Leader–Multiple-Follower (SLMF) and Multi-Leader–Multi-Follower (MLMF) Stackelberg game settings using three medical imaging datasets. Beyond node-level predictive performance, we assess fairness using Nash Social Welfare (NSW) and Weighted Nash Social Welfare (WNSW), which jointly capture efficiency and equity across heterogeneous participants. Our results show that ASWM improves the AUC of underrepresented nodes in the SLMF setup by an average of 1.87 percentage points over PWFedAvg and 0.88 percentage points over q-FFL, the strongest baseline, while nodes with larger datasets experience only a modest average change of −0.33 and +0.10 percentage points, respectively. More importantly, ASWM achieves the highest or near-highest NSW and WNSW values across the investigated datasets and configurations, indicating a more balanced and socially optimal distribution of performance. In the more complex MLMF setting, both ASWM and DSWM outperform the baseline aggregation methods at nearly all follower nodes, demonstrating that Stackelberg-based weighting mechanisms effectively mitigate data imbalance and promote fairness in decentralised learning environments with increased structural and data heterogeneity.