Reviews: Countering Feedback Delays in Multi-Agent Learning

If we accept that distributed learning is interesting, then this article presents a nice treatment of distributed mirror descent in which feedback may be asynchronous and delayed. Indeed, we are presented with a provably convergent learning algorithm for continuous action sets (in classes of games) even when individual players' feedback are received with differing levels of delay; further more the regret at time T is controlled as a function of the total delay to time T. This is a strong result, achieved by using a suite of very current proof techniques - lambda-Fenchel couplings serving as primula-dual Bregman divergences and associated tools. I have some concerns, but overall I think this is a good paper. If the concept of variational stability implies that all Nash equilibria of a game are in a closed and convex set, to me this is a major restriction on the class of games for which the result is relevant.