Distributed Learning for Online Stochastic Mixed Equilibrium Problems With Heavy-Tailed Noises.

Area of Science:

• Optimization Theory
• Distributed Systems
• Machine Learning

Background:

• Investigates mixed equilibrium problems (MEPs) in uncertain and dynamic environments.
• Utilizes a multiagent system (MAS) where agents have limited local information and communicate via a time-varying digraph.
• Addresses challenges of stochastic, time-varying bifunctions only revealed post-decision.

Purpose of the Study:

• To develop an online distributed learning algorithm for solving MEPs in complex environments.
• To analyze the algorithm's performance using dynamic regret.
• To establish theoretical bounds on regret, particularly under heavy-tailed noise conditions.

Main Methods:

• Employs a multiagent system (MAS) with decentralized decision-making.
• Proposes an online distributed learning algorithm integrating mirror descent and a clipping strategy.
• Analyzes dynamic regret against an offline benchmark, establishing high-probability bounds.

Main Results:

• The proposed algorithm achieves sublinear dynamic regret with high probability under heavy-tailed noise.
• Performance is validated theoretically, showing regret grows sublinearly if solution sequence variation is bounded.
• A simulation example confirms the theoretical findings.

Conclusions:

• The developed algorithm is effective for solving mixed equilibrium problems in uncertain and dynamic multiagent settings.
• The theoretical analysis provides strong guarantees on performance, even with noisy and changing data.
• The findings contribute to the understanding of distributed optimization in challenging environments.