Event-Triggered Distributed Stochastic Mirror Descent for Convex Optimization

Area of Science:

• Optimization Theory
• Networked Systems
• Distributed Computing

Background:

• Distributed optimization problems in multiagent networks face challenges with bandwidth limitations and communication costs.
• Existing methods often require frequent information exchange, straining network resources.

Purpose of the Study:

• To develop an efficient distributed optimization algorithm for time-varying multiagent networks considering non-Euclidean settings and bandwidth constraints.
• To reduce communication overhead through an event-triggered strategy.

Main Methods:

• An event-triggered strategy (ETS) was applied to manage information interaction between agents.
• A novel event-triggered distributed stochastic mirror descent (ET-DSMD) algorithm was proposed, using Bregman divergence.
• Convergence analysis of the ET-DSMD algorithm was performed.

Main Results:

• The ET-DSMD algorithm effectively addresses distributed convex constrained optimization problems.
• An upper bound on the convergence rate for each agent was established, dependent on the trigger threshold.
• Sublinear convergence is guaranteed if the trigger threshold approaches zero over time.

Conclusions:

• The developed ET-DSMD algorithm is feasible and efficient for resource-constrained multiagent optimization.
• The event-triggered approach significantly reduces communication costs while maintaining convergence properties.
• The study provides a theoretical framework and practical validation through a logistic regression example.