Abstract: This paper studies distributed optimization over undirected networks to minimize the average of local objective functions. Inspired by centralized adaptive gradient methods, we propose a novel distributed adaptive gradient tracking algorithm. The proposed algorithm enables each agent to adaptively update its step size using only local gradient information, completely eliminating the need for manual parameter tuning or global information about the objective functions. For smooth and strongly convex local objective functions, we prove that the generated iteration sequence converges linearly to the optimal solution. Numerical experiments on distributed linear regression problems demonstrate that, owing to a superior step-size update mechanism, the proposed algorithm achieves better convergence performance in comparison with existing distributed methods with fixed step sizes and adaptive step sizes.

Key words: distributed optimization, multi-agent networks, gradient tracking, adaptive method, step-size selection