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Understanding the Statistical Accuracy-Communication Trade-off in Personalized Federated Learning with Minimax Guarantees

ICML 2025 · Federated learning and privacy › Personalized and heterogeneous FL · approach: Personalization with global-local trade-off · 1 citations (OpenAlex)

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Analyzes the statistical accuracy and communication trade-off of a regularization-based personalized FL objective (global model plus local models coupled by a penalty λ), proving minimax-optimal local estimation rates and an accuracy-communication trade-off controlled by personalization degree.

Problem

Understanding how the personalization degree in regularization-based personalized federated learning quantitatively affects statistical accuracy of local models and communication/computation complexity, and their trade-off.

Approach

Analyzes the objective directly (without algorithm dependence) to derive non-asymptotic statistical rates for each local model as a function of the coupling parameter λ, shows minimax optimality of the resulting rate, and proposes FedCLUP, a bilevel algorithm whose communication complexity scales with λ, revealing the accuracy-communication trade-off.

Key results

• Theoretical statistical rate for local models interpolates between O(1/n) (local training) and O(1/N + R^2) (global collaboration), with minimax optimality matching the lower bound of O(1/N + R^2 ∧ 1/n) for suitable λ.
• FedCLUP communication complexity O(κ (λ+μ)/(λ+L) log(1/ε)) rounds and Õ(κ log(1/ε)) gradient evaluations, so smaller λ (more personalization) reduces communication without extra computation.
• On MNIST Logit, FedCLUP test accuracy rises from 0.8123 (high personalization) to 0.8312 (low personalization), approaching GlobalTrain's 0.8391.

Measured effects reported in the paper

Surprising findings

• On CIFAR10 CNN3 under high personalization, FedCLUP (0.6102) underperforms LocalTrain (0.6238), contrary to the general trend.

Limitations

• Theory assumes strong convexity and smoothness of the loss; non-convex results are only empirical.
• Extension to client-specific personalization degrees λ_i is left as open future work.
• Real-data step sizes use grid search since L is unknown, so the theoretical step-size choice is not directly applied.

Experimental setup

Datasets: MNIST EMNIST CIFAR10 Sent140 CelebA synthetic logistic regression data

Benchmarks: MNIST EMNIST CIFAR10 Sent140 CelebA synthetic data

Metrics: test accuracy training loss total error (squared distance to ground-truth model) communication rounds

Baselines: LocalTrain GlobalTrain pFedMe FedProx L2GD AL2SGD

Builds on: FedProx pFedMe L2GD Moreau envelope

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