Efficient Discrete-Time Distributed Least-Squares Algorithms Without Step-Size Tuning

Many distributed optimization algorithms critically depend on careful step-size tuning to ensure stability and achieve fast convergence. In this work, we address this limitation in the context of distributed algorithms for computing least-squares (LS) solutions to linear algebraic equations (LAEs). We consider two standard data-partitioning scenarios: (i) row-wise partitioning, where each agent has access to a row block of the coefficient matrix and the corresponding observation subvector, and (ii) column-wise partitioning, where each agent knows a column block of the coefficient matrix and a constituent of the observation vector. Leveraging a novel discretization strategy and the properties of semi-Schur matrices, we design discrete-time distributed LS algorithms for both scenarios that do not require step-size tuning. We provide a convergence analysis and show that the algorithms are always stable. Simulation results demonstrate that our methods double the communication efficiency and achieve faster convergence, shorter computation time per iteration, and smaller final error compared to state-of-the-art distributed LS algorithms.