Federated Composite Optimization

Federated Learning (FL) is a distributed learning paradigm which scales on-device learning collaboratively and privately. Standard FL algorithms such as Federated Averaging (FedAvg) are primarily geared towards smooth unconstrained settings. In this paper, we study the Federated Composite Optimization (FCO) problem, where the objective function in FL includes an additive (possibly) non-smooth component. Such optimization problems are fundamental to machine learning and arise naturally in the context of regularization (e.g., sparsity, low-rank, monotonicity, and constraint). To tackle this problem, we propose different primal/dual averaging approaches and study their communication and computation complexities. Of particular interest is Federated Dual Averaging (FedDualAvg), a federated variant of the dual averaging algorithm. FedDualAvg uses a novel double averaging procedure, which involves gradient averaging step in standard dual averaging and an average of client updates akin to standard federated averaging. Our theoretical analysis and empirical experiments demonstrate that FedDualAvg outperforms baselines for FCO.