Equilibria of Fully Decentralized Learning in Networked Systems

TL;DR

This paper investigates decentralized learning in networked systems, establishing equilibrium existence, proposing a learning mechanism, and validating results through simulations, thus advancing understanding of fully decentralized strategies.

Contribution

It introduces a simple structural condition for linear systems enabling decentralized learning and proves equilibrium existence, with a mechanism for agents to learn these equilibria.

Findings

Pure strategy Nash equilibria exist in the proposed game.

Simulations validate the theoretical results.

The mechanism enables agents to learn equilibria effectively.

Abstract

Existing settings of decentralized learning either require players to have full information or the system to have certain special structure that may be hard to check and hinder their applicability to practical systems. To overcome this, we identify a structure that is simple to check for linear dynamical system, where each player learns in a fully decentralized fashion to minimize its cost. We first establish the existence of pure strategy Nash equilibria in the resulting noncooperative game. We then conjecture that the Nash equilibrium is unique provided that the system satisfies an additional requirement on its structure. We also introduce a decentralized mechanism based on projected gradient descent to have agents learn the Nash equilibrium. Simulations on a $5$-player game validate our results.