Distributed Gradient-Free Mirror Descent Method with Edge-Based Event-Triggered Communication

This paper focuses on investigating the edge-based event-triggered distributed gradient-free mirror descent algorithm. To solve the complex problem of gradient calculation, a gradient-free oracle is introduced in the mirror descent method. Furthermore, an edge-based event-triggered strategy is applied to save communication resources, where the edge-based triggering condition controls local communications when the difference between the current state and the last triggered state is greater than the threshold. Based on this, the paper proposes an event-triggered distributed gradient-free mirror descent algorithm and also analyzes its convergence. Finally, the validity of the algorithm is verified on a distributed logistic regression problem.