Differentially Private Online Distributed Aggregative Games With Time-Varying and Non-Identical Communication and Feedback Delays

TL;DR

This paper introduces a novel online distributed algorithm for aggregative games that ensures privacy, handles time-varying and non-identical communication and feedback delays, and guarantees convergence with low regret.

Contribution

It is the first to address privacy concerns with non-uniform delays in aggregative games using an online dual averaging approach.

Findings

Convergence of local actions over time demonstrated in simulations.

Achieves low regret bounds despite delays and privacy constraints.

Handles unbalanced communication graphs with time-varying delays.

Abstract

This paper investigates online distributed aggregative games with time-varying cost functions, where agents are interconnected through an unbalanced communication graph. Due to the distributed and noncooperative nature of the game, some curious agents may wish to steal sensitive information from neighboring agents during parameter exchanges. Additionally, communication delays arising from network congestion, particularly in wireless settings, as well as feedback delays, can hinder the convergence of agents to a Nash equilibrium. Although a recent work addressed both communication and feedback delays in aggregative games, it is based on the unrealistic assumption that the delays are fixed over time and identical across agents. Hence, the case of time-varying and non-identical delays across agents has never been considered in aggregative games. In this work, we address the combined challenges of privacy leakage with time-varying and non-identical communication and feedback delays for the first time. We propose an online distributed dual averaging algorithm that simultaneously tackles these challenges while achieving a provably low regret bound. Our simulation result shows that the running average of each client's local action converges over time.