Personalized federated composite learning with forward-backward envelopes

Jiang Hu, Jinhyun Ahn, Na Li, Quanzheng Li

Keywords: Federated composite optimization, personalization, forward-backward envelopes

Abstract: Federated composite optimization (FCO) is an optimization problem in federated learning whose loss function contains a non-smooth regularizer. It arises naturally in the applications of federated learning (FL) that involve requirements such as sparsity, low rankness, and monotonicity. In this study, we propose a personalization method, called pFedFBE, for FCO by using forward-backward envelope (FBE) as clients’ loss functions. With FBE, we not only decouple the personalized model from the global model, but also allow personalized models to be smooth and easily optimized. In spite of the nonsmoothness of FCO, pFedFBE shows the same convergence complexity results as FedAvg for FL with unconstrained smooth objectives. Numerical experiments are shown to demonstrate the effectiveness of our proposed method.

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