Distributed stochastic dual averaging algorithm over time-varying networks with communication noises

Distributed optimization over noisy networks is a challenging problem that requires efficient communication and cooperation among agents. This paper proposes a distributed stochastic dual averaging algorithm under the two-time-scale approach (DSDAA-TTS) to solve distributed constrained optimization problems over time-varying networks with noises. In DSDAA-TTS, one time-scale is used as the step size of the algorithm, while the other is used to decrease the effect of noises. This paper proves that, under a general condition on communication noises, the expected and high probability convergence rates of DSDAA-TTS are [Formula presented] under appropriate choices of the two-time-scale approach. Moreover, the deterministic case of DSDAA-TTS with subgradient information and upper-bounded noises is investigated. This mathematical model is applied to the static quantization and the event-trigger (constant trigger threshold) schemes for illustration.