Federated Multi-Objective Learning

TL;DR

This work extends multi-objective optimization to federated settings by introducing the Federated Multi-Objective Learning (FMOL) framework, which accommodates objective and data heterogeneity across distributed clients. It proposes two gradient-based FMOO algorithms, FMGDA and FSMGDA, that use local updates and a convex quadratic projection to derive a common descent direction, achieving convergence rates matching centralized MOO: linear or exp(−μT) in strongly convex cases and O(1/T) or O(1/√T) in non-convex cases, depending on whether full or stochastic gradients are used. A milder (α, β)-Lipschitz stochastic-gradient assumption underpins the FSMGDA analysis, enabling robust guarantees with practical gradient noise models. Empirical results on MultiMNIST, River Flow, and CelebA corroborate the theoretical findings, demonstrating communication-efficient training and resilience to data and objective heterogeneity in federated, multi-task scenarios.

Abstract

In recent years, multi-objective optimization (MOO) emerges as a foundational problem underpinning many multi-agent multi-task learning applications. However, existing algorithms in MOO literature remain limited to centralized learning settings, which do not satisfy the distributed nature and data privacy needs of such multi-agent multi-task learning applications. This motivates us to propose a new federated multi-objective learning (FMOL) framework with multiple clients distributively and collaboratively solving an MOO problem while keeping their training data private. Notably, our FMOL framework allows a different set of objective functions across different clients to support a wide range of applications, which advances and generalizes the MOO formulation to the federated learning paradigm for the first time. For this FMOL framework, we propose two new federated multi-objective optimization (FMOO) algorithms called federated multi-gradient descent averaging (FMGDA) and federated stochastic multi-gradient descent averaging (FSMGDA). Both algorithms allow local updates to significantly reduce communication costs, while achieving the {\em same} convergence rates as those of their algorithmic counterparts in the single-objective federated learning. Our extensive experiments also corroborate the efficacy of our proposed FMOO algorithms.

Figures (6)

• Figure 1: Training loss convergence comparison.
• Figure 2: Training losses comparison
• Figure 3: Experiments on CelebA dataset.
• Figure 4: Experiments on i.i.d. data.
• Figure 5: Loss value comparisons of algorithms on a different numbers of clients $M$.

Theorems & Definitions (24)

• Definition 1: (Weak) Pareto Optimality
• Definition 2: Pareto Stationarity
• theorem 1: FMGDA for Non-convex FMOL
• Corollary 1
• theorem 2: FMGDA for $\mu$-Strongly Convex FMOL
• Corollary 2
• theorem 3: FSMGDA for Non-convex FMOL
• Corollary 3
• theorem 4: FSMGDA for $\mu$-Strongly Convex FMOL
• Corollary 4