Online Learning Algorithm for Distributed Convex Optimization With Time-Varying Coupled Constraints and Bandit...

Area of Science:

• Optimization and Control Theory
• Distributed Systems
• Machine Learning

Background:

• Multiagent systems face challenges in dynamic environments with time-varying costs and constraints.
• Individual agents often lack complete information about global cost and constraint functions.

Purpose of the Study:

• To develop novel distributed online learning algorithms for multiagent constrained optimization.
• To analyze algorithm performance in both gradient-feedback and gradient-free settings.
• To demonstrate effectiveness using simulations, such as electric vehicle charging.

Main Methods:

• A distributed primal-dual online learning algorithm for the gradient-feedback scenario.
• A bandit-based extension for the gradient-free scenario, utilizing function value queries.
• Theoretical analysis establishing sublinear bounds on regret and constraint violations.

Main Results:

• The gradient-feedback algorithm achieves sublinear regret and constraint violation bounds.
• The gradient-free (bandit) algorithm demonstrates comparable performance to the gradient-feedback approach under challenging conditions.
• Numerical simulations confirm the practical efficacy of both proposed algorithms.

Conclusions:

• Distributed online learning algorithms can effectively address complex optimization problems in dynamic multiagent systems.
• The gradient-free approach offers a viable alternative when gradient information is unavailable or costly.
• The developed methods show promise for real-world applications like smart grids and resource management.