Online Federated Composite Optimization with Multiple Kernels

This paper focuses on Online Federated Composite Optimization (OFCO) problem, where the loss function con-tains a non-smooth regularizer and the network environment is time-varying. This problem is prevalent in various real-world applications, spanning from wireless sensor networks to signal processing. To address the challenge posed by OFCO, we propose a novel federated learning algorithm, named FedOE, which draws inspiration from approximate composite mirror descent. Furthermore, FedOE incorporates a multi-kernel strategy to enhance accuracy and flexibility, emphasizing a comprehensive and effective solution to the OFCO problem. Through theoretical analysis, FedOE achieves a regularized regret on the order of O(VT) with the total number of rounds T. Finally, the numerical experiments validate the efficacy of the proposed algorithm.