FedHV: Low-Overhead Hypervolume Weighting for Federated Multi-Objective Optimization

2026-09-26

AI Summary

This study addresses the high communication overhead and additional synchronization requirements in federated multi-objective optimization by proposing the FedHV algorithm. This method introduces the first closed-form inverse relaxation weighting mapping, reducing communication complexity to Θ(d+m) by transmitting only a few scalars without extra synchronization phases, thereby completely eliminating server-side iterative optimization. Theoretically, by integrating hypervolume weighting with reference-relative objective relaxation analysis, the convergence of single-round delayed weights is established. Experimental results demonstrate that across multiple non-IID vision benchmarks, FedHV significantly outperforms baseline methods such as FSMGDA in both average accuracy and worst-task accuracy.

Abstract

Task-wise federated multi-objective optimization (FedMOO) trains a shared model for competing prediction objectives under heterogeneous data, partial participation, and communication constraints. Existing methods commonly derive task weights from gradient or update geometry. This requires task-specific information or iterative server-side optimization. We introduce FedHV, which maps reference-relative objective slacks to closed-form inverse-slack weights. Each client optimizes one weighted loss and returns objective estimates with its model update. The protocol adds exactly 2m auxiliary scalars per participating client, yielding Theta(d + m) total per-client communication, compared with the Theta(md) task-specific communication of FSMGDA, and requires no additional synchronization stage. We analyze the resulting one-round-delayed weights under client heterogeneity, multi-step local updates, partial participation, and finite-sample objective reports. Under a fixed-horizon positive-slack reference condition, with the prescribed horizon-dependent step size and vanishing report error, FedHV achieves an O(T^(-1/2)) rate for the average squared log-hypervolume gradient norm; persistent report error determines the resulting stationarity neighborhood. The same bound controls the squared Pareto-stationarity residual. Across six Dirichlet-partitioned non-IID settings from four vision benchmark families and three training seeds, FedHV exceeds FSMGDA and FedCMOO in mean accuracy in five settings. Among these methods and uniform scalarization, it achieves the highest worst-task accuracy in four settings and improves the difficult CIFAR-10 objective in both CIFAR10-MNIST settings.

Problem

• Federated Multi-Objective Optimization
• Communication Overhead
• Client Heterogeneity
• Partial Participation
• Hypervolume Weighting

Innovation

• Federated Multi-Objective Optimization
• Hypervolume Weighting
• Low Communication Overhead
• Pareto Stationarity
• Closed-form Inverse-Slack Weights