Federated Composite Optimization
This addresses a bottleneck in federated learning for applications with constraints like sparsity, offering an incremental improvement over existing methods.
The paper tackles the Federated Composite Optimization problem, where loss functions include non-smooth regularizers, by proposing Federated Dual Averaging (FedDualAvg), which outperforms baselines by circumventing the curse of primal averaging.
Federated Learning (FL) is a distributed learning paradigm that scales on-device learning collaboratively and privately. Standard FL algorithms such as FedAvg are primarily geared towards smooth unconstrained settings. In this paper, we study the Federated Composite Optimization (FCO) problem, in which the loss function contains a non-smooth regularizer. Such problems arise naturally in FL applications that involve sparsity, low-rank, monotonicity, or more general constraints. We first show that straightforward extensions of primal algorithms such as FedAvg are not well-suited for FCO since they suffer from the "curse of primal averaging," resulting in poor convergence. As a solution, we propose a new primal-dual algorithm, Federated Dual Averaging (FedDualAvg), which by employing a novel server dual averaging procedure circumvents the curse of primal averaging. Our theoretical analysis and empirical experiments demonstrate that FedDualAvg outperforms the other baselines.