Distributed Online Constrained Optimization With Feedback Delays.

Area of Science:

• Distributed Optimization
• Convex Optimization
• Control Theory

Background:

• Real-world systems often involve agents making decisions with delayed information.
• Cooperative optimization requires minimizing shared costs under coupled constraints.
• Networked systems with dynamic communication topologies present significant challenges.

Purpose of the Study:

• To develop and analyze a distributed algorithm for online constrained convex optimization with feedback delays.
• To address challenges posed by time-varying communication and delayed information.
• To ensure cooperative minimization of local costs subject to coupled constraints.

Main Methods:

• A distributed online primal-dual bandit push-sum algorithm was employed.
• The algorithm generates primal and dual variables incorporating delayed feedback.
• Performance was analyzed using expected regret and expected constraint violation metrics.

Main Results:

• The proposed algorithm achieves sublinear expected regret.
• Sublinear expected constraint violation was demonstrated.
• Theoretical results were validated through simulations on a power grid optimization problem.

Conclusions:

• The developed algorithm is effective for multiagent distributed online constrained convex optimization with feedback delays.
• The sublinear performance guarantees hold under time-varying network conditions.
• The approach provides a robust solution for practical applications like power grid management.