Semi Bandit Dynamics in Congestion Games: Convergence to Nash Equilibrium and No-Regret Guarantees

TL;DR

This paper presents a new online gradient descent variant for congestion games that guarantees convergence to Nash Equilibrium and sublinear regret, with efficiency independent of the exponential action set size.

Contribution

Introduces a novel online gradient descent method for congestion games that achieves convergence and regret guarantees with polynomial dependence on game parameters.

Findings

Proves convergence to Nash Equilibrium in congestion games.

Achieves sublinear regret in semi-bandit feedback setting.

Method's complexity depends polynomially on game size, not action set size.

Abstract

In this work, we introduce a new variant of online gradient descent, which provably converges to Nash Equilibria and simultaneously attains sublinear regret for the class of congestion games in the semi-bandit feedback setting. Our proposed method admits convergence rates depending only polynomially on the number of players and the number of facilities, but not on the size of the action set, which can be exponentially large in terms of the number of facilities. Moreover, the running time of our method has polynomial-time dependence on the implicit description of the game. As a result, our work answers an open question from (Du et. al, 2022).