Improved Convergence Rate for a Distributed Two-Time-Scale Gradient Method under Random Quantization
Marcos M. Vasconcelos, Thinh T. Doan, Urbashi Mitra · 2021 60th IEEE Conference on Decision and Control (CDC) · 2021
We study the so-called distributed two-time-scale gradient method for solving convex optimization problems over a network of agents when the communication bandwidth between the nodes is limited. Therefore, information exchanged between the nodes must be quantized. Our main contribution is to provide a novel analysis, resulting in an improved convergence rate of this method compared to existing works. In particular√, we show that the method converges at a rate $\mathcal{O}\left( {{{\log }^2}(k)/\sqrt k } \right)$ to the optimal solution when the underlying objective function is strongly convex and smooth. The essential technique in our analysis is to consider a Lyapunov function that simultaneously captures the coupling of the consensus and optimality errors generated by the method.