Personalized Aggregation (pFedMe)

pFedMe reformulates the federated learning objective using Moreau envelopes, a mathematical tool from convex optimization. This creates a bi-level optimization problem where each client optimizes a personalized model in the inner loop while the server aggregates global knowledge in the outer loop. The Moreau envelope acts as a smooth approximation of the local loss function, allowing the personalized model to stay close to the global model while adapting to local data distributions. This decoupling is critical for handling statistical heterogeneity across clinical sites.

The personalization mechanism in pFedMe is driven by an L2 regularization term that penalizes the distance between the local personalized model and the global model. This penalty is controlled by a hyperparameter λ that balances two competing objectives:

• Small λ: Allows the local model to deviate significantly, capturing site-specific patterns in clinical data
• Large λ: Keeps the local model close to the global consensus, leveraging shared knowledge across institutions This provides a tunable knob for clinical informatics directors to control the degree of personalization.

pFedMe employs Nesterov accelerated gradient descent in the inner optimization loop to solve each client's personalized subproblem efficiently. Nesterov acceleration provides a look-ahead mechanism that computes gradients at a projected future position rather than the current position, achieving an optimal convergence rate of O(1/k²) for smooth convex functions. This reduces the number of local computation rounds required per communication round, directly lowering the computational burden on resource-constrained clinical edge devices.

pFedMe achieves communication efficiency through its decoupled optimization structure. Unlike FedAvg, which requires frequent synchronization of model weights, pFedMe allows clients to solve their personalized subproblems to high accuracy locally before communicating. This reduces the total number of communication rounds needed for convergence. The algorithm transmits only the global model parameters between server and clients, while personalized parameters remain local, further minimizing bandwidth overhead in bandwidth-constrained hospital networks.

pFedMe provides rigorous convergence guarantees under realistic federated conditions. The algorithm provably converges for both strongly convex and non-convex loss functions, which covers most practical deep learning architectures used in medical imaging and EHR analysis. The convergence analysis accounts for:

• Statistical heterogeneity (non-IID data across hospitals)
• System heterogeneity (varying compute capabilities of clinical devices)
• Partial client participation (only a subset of hospitals available per round) These guarantees are essential for regulatory compliance in healthcare AI deployments.

pFedMe offers distinct advantages over baseline aggregation algorithms:

• vs FedAvg: FedAvg produces a single global model that may perform poorly on outlier clinical populations. pFedMe generates personalized models per site while still benefiting from collaborative learning.
• vs FedProx: FedProx adds a proximal term to stabilize training but still optimizes for a single global model. pFedMe's Moreau envelope formulation provides stronger theoretical guarantees and explicit personalization.
• vs Fine-tuning: Unlike naive fine-tuning of a global model on local data, pFedMe's bi-level optimization prevents catastrophic forgetting of globally learned features.