We show that the augmented primal-dual gradient algorithms can achieve global exponential convergence with partially strongly convex functions. In particular, the objective function only needs to be strongly convex in the subspace satisfying the equality constraint and can be generally convex elsewhere, provided the global Lipschitz condition for the gradient is satisfied. This condition implies that states outside the equality subspace will converge towards it exponentially fast. The analysis is then applied to distributed optimization, where the partially strong convexity can be relaxed to the restricted secant inequality condition, which is not necessarily convex. This work unifies global exponential convergence results for some existing centralized and distributed algorithms. © 2025 AACC.

We propose a robust aggregation method for model parameters in federated learning (FL) under noisy communications. FL is a distributed machine learning paradigm in which a central server aggregates local model parameters from multiple clients. These parameters are often noisy and/or have missing values during data collection, training, and communication between the clients and server. This may cause a considerable drop in model accuracy. To address this issue, we learn a graph that represents pairwise relationships between model parameters of the clients during aggregation. We realize it with a joint problem of graph learning and signal (i.e., model parameters) restoration. The problem is formulated as a difference-of-convex (DC) optimization, which is efficiently solved via a proximal DC algorithm. Experimental results on MNIST and CIFAR10 datasets show that the proposed method outperforms existing approaches by up to 2-5% in classification accuracy under biased data distributions and noisy conditions. © 2025 IEEE.

This paper proposes a method for designing directed graph (digraph) filters through a dictionary learning approach. Practical digraph filtering methods have not yet been established because of the difficulties posed by asymmetry of the adjacency matrix of a digraph. Augmented graph Fourier transform (AuGFT), proposed by Kitamura et al., defines a new graph Laplacian and extends the conventional graph Fourier transform (GFT) for undirected graph signals to directed ones. However, challenges remain in filter design through AuGFT, particularly in determining the skew intensity parameters. Therefore, this study aims to establish a design method for digraph filters with AuGFT. Filters are parameterized with AuGFT, and parameter optimization is performed using a dictionary learning technique. To verify the effectiveness of the proposed method, experimental results of digraph filtering are shown for temperature data of contiguous US and the GSP-traffic-dataset. Compared with undirected graph filtering, the proposed method is shown to have high steerability in designing digraph filters. © 2024 IEEE.