Distributed Constrained Online Optimization with Noisy Communication

This paper addresses distributed online optimization problems with time-varying coupled constraints via a group of cooperative agents. The communication among agents suffers from disturbance of noise. By employing primal-dual mirror descent method, we propose a distributed online algorithm with noisy communication for solving such problems. By using the bound of noise, we obtain estimations on both dynamic regret and constraint violation, which depict the effect of communication noise. Then, by choosing certain diminishing step sizes, we theoretically prove that the dynamic regret and constraint violation grow sublinearly, provided that the optimal decision sequence varies slowly and the noise is attenuated. Finally, theoretical results is substantiated by a numerical example.