Distributed Online Mirror Descent Algorithm with Event Triggered Communication

The paper proposes an algorithm that uses distributed online mirror descent algorithm for solving constrained online optimization problem with event triggered communication. The optimization is over a time horizon and the future objective functions are not apriori known to each agent. In the proposed algorithm, the communication between the agents, that happens in a distributed optimization framework, occurs only when the difference between the current state and the state when the last event has been triggered exceeds a threshold. The performance of the algorithm is analysed using a regret function. We establish a bound on the regret and provide sufficient conditions on the step-size and thresholding error such that the regret is sublinear. We demonstrate the reduction in the number of inter-agent communications using our proposed algorithm for an estimation problem in a dynamic environment.