Offline congestion games: How feedback type affects data coverage requirement

TL;DR

This paper explores how different feedback types in offline congestion games influence the ability to efficiently recover approximate Nash Equilibria, revealing fundamental differences and limitations across feedback models.

Contribution

It introduces new coverage conditions and algorithms for recovering approximate NE under various feedback settings, establishing the first formal analysis of offline congestion games.

Findings

Facility-level feedback allows NE recovery with a novel coverage condition.

Agent-level feedback requires a generalized data coverage assumption for linear bandits.

Game-level feedback needs a stronger coverage assumption for NE recovery.

Abstract

This paper investigates when one can efficiently recover an approximate Nash Equilibrium (NE) in offline congestion games. The existing dataset coverage assumption in offline general-sum games inevitably incurs a dependency on the number of actions, which can be exponentially large in congestion games. We consider three different types of feedback with decreasing revealed information. Starting from the facility-level (a.k.a., semi-bandit) feedback, we propose a novel one-unit deviation coverage condition and give a pessimism-type algorithm that can recover an approximate NE. For the agent-level (a.k.a., bandit) feedback setting, interestingly, we show the one-unit deviation coverage condition is not sufficient. On the other hand, we convert the game to multi-agent linear bandits and show that with a generalized data coverage assumption in offline linear bandits, we can efficiently recover the approximate NE. Lastly, we consider a novel type of feedback, the game-level feedback where only the total reward from all agents is revealed. Again, we show the coverage assumption for the agent-level feedback setting is insufficient in the game-level feedback setting, and with a stronger version of the data coverage assumption for linear bandits, we can recover an approximate NE. Together, our results constitute the first study of offline congestion games and imply formal separations between different types of feedback.