Federated Learning with Convex Global and Local Constraints.

Area of Science:

• Machine Learning
• Distributed Systems
• Optimization

Background:

• Federated learning (FL) is crucial for collaborative machine learning (ML) with distributed sensitive data, such as in healthcare.
• Existing FL techniques primarily address unconstrained problems or those with simple constraints, leaving a gap for general constraint handling.
• Practical ML applications often involve complex constraints that are not easily managed by current FL algorithms.

Purpose of the Study:

• To develop a general algorithmic framework for solving federated learning problems with arbitrary constraints.
• To propose a novel FL algorithm capable of handling complex, non-projection-friendly constraints.
• To analyze the theoretical performance and demonstrate the practical utility of the new algorithm.

Main Methods:

• Development of a new FL algorithm based on the proximal augmented Lagrangian (AL) method.
• Theoretical analysis of the algorithm's worst-case complexity under convex objectives and constraints.
• Empirical validation through numerical experiments on specific constrained ML tasks.

Main Results:

• The proposed proximal augmented Lagrangian-based FL algorithm effectively handles general constraints.
• Theoretical analysis provides insights into the algorithm's convergence properties under specific conditions.
• Numerical experiments confirm the algorithm's efficacy in challenging FL applications like Neyman-Pearson classification and fairness-aware learning.

Conclusions:

• The developed algorithmic framework represents a significant step forward in addressing constrained FL problems.
• The proposed method offers a viable solution for real-world FL applications involving complex constraints and sensitive data.
• This work paves the way for more robust and versatile federated learning systems.