Precise complexity of sparse discounted CCE computation

Determine the precise computational complexity of computing sparse coarse correlated equilibria in discounted Markov games, thereby resolving the gap between the quasi-polynomial upper bounds and the computational lower bounds established for this task.

Background

The paper develops radically uncoupled learning algorithms for general-sum discounted Markov games with quasi-polynomial convergence and computational guarantees. It also proves, under the Exponential Time Hypothesis for PPAD, that no polynomial-time algorithm can compute sufficiently accurate sparse discounted coarse correlated equilibria for certain discounted Markov games.

Consequently, the current results leave a complexity gap: the available upper bounds are quasi-polynomial, while the lower bounds rule out polynomial time but do not establish whether the problem is complete for a particular complexity class or whether the quasi-polynomial upper bounds are essentially optimal. The authors explicitly identify closing this gap as an important open problem.