DREAM: A Unified Framework for Drift-Corrected Federated Multi-Objective Learning

Federated Multi-Objective Learning (FMOL) enables collaborative training of conflicting objectives but faces a compounded challenge: the recursive coupling between intra-task client drift and inter-task aggregation bias. We propose DREAM, a unified framework that jointly corrects these two coupled error sources through drift-aware control variates and momentum-smoothed local updates. On the server side, DREAM formulates multi-objective aggregation as a regularized quadratic program parameterized by a task correction matrix, which provides a generalized formulation that can flexibly adapt to scalarization, prioritization, and gradient manipulation strategies. Theoretically, we establish a linear speedup convergence rate of $\mathcal{O}(1/\sqrt{NT})$ for non-convex objectives. We further provide theoretical guarantees for the conflict-avoidant direction distance. In the strongly convex setting, DREAM achieves convergence in weighted sub-optimality and admits a unified Lyapunov analysis showing linear convergence to a regularization-dependent neighborhood. Numerical experiments on representative benchmarks validate the effectiveness of DREAM in multi-objective optimization.

Federated Multi-Objective Learning (FMOL) studies how decentralized clients collaboratively train one model for several conflicting objectives, such as multiple related prediction tasks. In heterogeneous FMOL, each client may see different data, so local training can cause intra-task client drift: the task-wise updates sent to the server move away from the true global directions. This drift becomes especially harmful because multi-objective aggregation chooses task weights through a nonlinear solver; drifted inputs can therefore be amplified into inter-task aggregation bias and lead to poor Pareto trade-offs. We propose DREAM, a drift-corrected and momentum-smoothed framework for FMOL. DREAM uses task-wise control variates to correct systematic client drift and momentum-smoothed local updates to reduce stochastic oscillations before aggregation. On the server, DREAM computes multi-objective task weights with a regularized quadratic program and a task correction matrix, allowing the same framework to support scalarization, task prioritization, and task-interaction modeling. We prove convergence guarantees for both non-convex and strongly convex objectives, including guarantees on the conflict-avoidant direction distance. Experiments on Multi-MNIST, CIFAR-100, and CelebA show that DREAM improves task balance, robustness to local training, and overall performance compared with representative FMOL baselines.