On the Convergence Rates of A Nash Equilibrium Seeking Algorithm in Potential Games with Information Delays

TL;DR

This paper analyzes how a modified accelerated gradient descent algorithm converges to Nash equilibria in potential games with continuous strategies, considering feedback delays and providing convergence rates under various delay growth conditions.

Contribution

It extends accelerated gradient methods to multi-agent potential games with delays, deriving convergence rates based on delay growth patterns and tuning parameters.

Findings

Convergence rates are established for sublinear, linear, and superlinear delay growth.

Proper tuning of step sizes ensures convergence despite delays.

Simulations confirm theoretical results in a routing game scenario.

Abstract

This paper investigates the equilibrium convergence properties of a proposed algorithm for potential games with continuous strategy spaces in the presence of feedback delays, a main challenge in multi-agent systems that compromises the performance of various optimization schemes. The proposed algorithm is built upon an improved version of the accelerated gradient descent method. We extend it to a decentralized multi-agent scenario and equip it with a delayed feedback utilization scheme. By appropriately tuning the step sizes and studying the interplay between delay functions and step sizes, we derive the convergence rates of the proposed algorithm to the optimal value of the potential function when the growth of the feedback delays in time is subject to sublinear, linear, and superlinear upper bounds. Finally, simulations of a routing game are performed to empirically verify our findings.