Optimization, Communication, and Personalization in Federated Learning for Massive Networks

We consider the problem of collaborative model optimization over a distributed network of agents, each possessing locally held data drawn from potentially heterogeneous distributions. The system operates under constraints of limited communication, partial participation, and privacy preservation, thereby necessitating the design of algorithms that balance local computation and global aggregation. We investigate the convergence properties and trade-offs arising in such iterative optimization schemes, where updates are performed asynchronously or synchronously, and communication overheads are mitigated via compression or quantization techniques. The objective is to characterize the interplay between model fidelity, communication complexity, and heterogeneity of local objective functions. We explore frameworks that enable personalized solutions tailored to individual agents while leveraging shared representations, often framed as multi-task or meta-optimization problems. Incentive structures are incorporated to model rational agent behavior under resource constraints and strategic participation, formalized through utility maximization and game-theoretic constructs. This work lays a foundation for understanding the fundamental limits and algorithmic principles governing scalable distributed learning systems, emphasizing theoretical guarantees alongside system-level considerations. Our approach highlights open questions concerning the balance of privacy, robustness, and efficiency in decentralized optimization, motivating future exploration into principled design and analysis of federated learning methodologies.