[Paper Review] Federated Learning Meets Multi-objective Optimization

Zeou Hu, Kiarash Shaloudegi+2 more|arXiv (Cornell University)|Jun 20, 2020

Privacy-Preserving Technologies in Data35 references31 citations

TL;DR

The paper formulates federated learning as multi-objective optimization and introduces FedMGDA+, an algorithm that converges to Pareto stationary solutions and balances accuracy, fairness, and robustness in distributed edge learning.

ABSTRACT

Federated learning has emerged as a promising, massively distributed way to train a joint deep model over large amounts of edge devices while keeping private user data strictly on device. In this work, motivated from ensuring fairness among users and robustness against malicious adversaries, we formulate federated learning as multi-objective optimization and propose a new algorithm FedMGDA+ that is guaranteed to converge to Pareto stationary solutions. FedMGDA+ is simple to implement, has fewer hyperparameters to tune, and refrains from sacrificing the performance of any participating user. We establish the convergence properties of FedMGDA+ and point out its connections to existing approaches. Extensive experiments on a variety of datasets confirm that FedMGDA+ compares favorably against state-of-the-art.

Motivation & Objective

• Motivate fairness and robustness challenges in federated learning with heterogeneous user data and limited communication.
• Introduce a multi-objective optimization perspective for FL where each user’s loss is an objective.
• Develop an algorithm (FedMGDA+) that guarantees convergence to Pareto stationary solutions.
• Provide theoretical convergence guarantees under mild assumptions.
• Demonstrate empirical effectiveness and robustness of FedMGDA+ across diverse datasets and settings.

Proposed method

• Model each user’s loss f_i as an objective in a multi-objective minimization problem MOP.
• Extend the multiple gradient descent algorithm (MGDA) to FL to find a descent direction that minimizes a convex combination of gradients.
• Compute the optimal dual weights lambda_t by solving a simple quadratic program on the gradient hull (min-norm direction).
• Normalize gradients to enhance robustness against adversarial manipulation and to stabilize updates.
• Allow multiple local updates per round to balance communication and computation, with subsampling of clients to mitigate non-iid effects.
• Prove convergence to Pareto stationary solutions under Lipschitz smoothness and mild conditions (Theorem 1a, 1b, 2).

Experimental results

Research questions

• RQ1 Can federated learning be effectively framed as a multi-objective optimization problem across participating clients?
• RQ2 Can an MGDA-based update (FedMGDA+) provide a common descent direction that improves all client objectives without sacrificing any?
• RQ3 What convergence guarantees can be established for FedMGDA+ in FL with non-iid data and partial participation?
• RQ4 How do fairness, robustness, and accuracy trade-offs behave under FedMGDA+ compared to existing FL methods?
• RQ5 Do empirical results on real datasets support the theoretical advantages of FedMGDA+ in FL settings?

Key findings

• FedMGDA+ converges to Pareto stationary solutions under mild assumptions (Theorems 1a and 1b).
• The method automatically tunes client weights via a dual optimization, balancing average performance and fairness without sacrificing any participating client.
• Gradient normalization enhances robustness against malicious clients and contributes to stable convergence.
• Subsampling and local update schemes are compatible with FedMGDA+, preserving descent directions and enabling scalable FL.
• Empirical results show FedMGDA+ is competitive with state-of-the-art methods across metrics like accuracy, fairness, and robustness (as summarized in the experiments).
• The paper provides connections between FedMGDA+ and existing FL algorithms, and offers theoretical insights into MoM perspectives for FL.