[논문 리뷰] Personalized Federated Learning with Moreau Envelopes

Canh T. Dinh, Nguyen H. Tran외 1명|arXiv (Cornell University)|2020. 06. 16.

Privacy-Preserving Technologies in Data참고 문헌 56인용 수 214

한 줄 요약

pFedMe를 소개하며 Moreau 엔벨로프를 이용해 개인화된 모델 최적화를 글로벌 모델 학습으로부터 분리하는 개인화된 연합 학습 알고리즘으로, FedAvg 및 Per-FedAvg에 비해 수렴 속도 및 로컬 정확도가 최적 수준이며 개선된 성능을 보임.

ABSTRACT

Federated learning (FL) is a decentralized and privacy-preserving machine learning technique in which a group of clients collaborate with a server to learn a global model without sharing clients' data. One challenge associated with FL is statistical diversity among clients, which restricts the global model from delivering good performance on each client's task. To address this, we propose an algorithm for personalized FL (pFedMe) using Moreau envelopes as clients' regularized loss functions, which help decouple personalized model optimization from the global model learning in a bi-level problem stylized for personalized FL. Theoretically, we show that pFedMe's convergence rate is state-of-the-art: achieving quadratic speedup for strongly convex and sublinear speedup of order 2/3 for smooth nonconvex objectives. Experimentally, we verify that pFedMe excels at empirical performance compared with the vanilla FedAvg and Per-FedAvg, a meta-learning based personalized FL algorithm.

연구 동기 및 목표

• 개인화를 가능하게 하여 연합학습에서 클라이언트 간의 non-i.i.d. 데이터를 다룬다.
• Moreau 엔벨로프를 사용하여 글로벌 모델 업데이트와 개인화된 모델 업데이트를 분리하는 이중 최적화 문제를 수식화한다.
• 강볼록 및 비볼록 목적함수에 대한 수렴 속도를 입증한다.
• 실제 및 합성 데이터셋에서 pFedMe를 FedAvg 및 Per-FedAvg와 실증적으로 검증한다.

제안 방법

• Formulate a bi-level optimization where F(w)=1/N sum Fi(w) and Fi(w)=min_thetai { fi(theta_i) + (lambda/2) ||theta_i - w||^2 }.
• Use Moreau envelopes to derive the proximal-like personalized updates and a gradient-based outer update for the global model.
• At each round, perform R local steps to optimize theta_i(w) via delta-approximation tilde_theta_i, then update w via gradient of Fi with respect to w.
• Provide convergence analysis for strongly convex and nonconvex smooth settings, establishing quadratic and 2/3 sublinear speedups under respective assumptions.
• Compare pFedMe with FedAvg and Per-FedAvg on MNIST and synthetic data, examining hyperparameters R, K, |D|, lambda, and beta.

실험 결과

연구 질문

• RQ1 How can Moreau envelopes be leveraged to decouple personalized model optimization from global model learning in FL?
• RQ2 What convergence rates can be achieved for pFedMe under strongly convex and nonconvex objectives?
• RQ3 Does pFedMe provide better local (personalized) performance and/or faster convergence than FedAvg and Per-FedAvg in non-i.i.d. settings?
• RQ4 How do hyperparameters (R, K, |D|, lambda, beta) affect performance and convergence?

주요 결과

• pFedMe achieves state-of-the-art convergence speeds: quadratic speedup for strongly convex and 2/3 sublinear speedup for smooth nonconvex objectives.
• Empirically, pFedMe’s personalized models outperform FedAvg and Per-FedAvg in local accuracy and convergence rate on MNIST and synthetic data.
• The Moreau envelope-based formulation effectively decouples personalized optimization from global learning, enabling parallelized updates.
• Delta-approximation of the inner minimizer and first-order gradients suffice, avoiding Hessian computations as in other meta-learning approaches.
• Hyperparameter tuning shows larger R can improve convergence but trades off computation; appropriate lambda balances personalization and global alignment.