Load balancing without regret in the bulletin board model

Abstract

We analyze the performance of protocols for load balancing in distributed systems based on no-regret algorithms from online learning theory. These protocols treat load balancing as a repeated game and apply algorithms whose average performance over time is guaranteed to match or exceed the average performance of the best strategy in hindsight. Our approach captures two major aspects of distributed systems. First, in our setting of atomic load balancing, every single process can have a significant impact on the performance and behavior of the system. Furthermore, although in distributed systems participants can query the current state of the system they cannot reliably predict the effect of their actions on it. We address this issue by considering load balancing games in the bulletin board model, where players can find out the delay on all machines, but do not have information on what their experienced delay would have been if they had selected another machine. We show that under these more realistic assumptions, if all players use the well-known multiplicative weights algorithm, then the quality of the resulting solution is exponentially better than the worst correlated equilibrium, and almost as good as that of the worst Nash. These tighter bounds are derived from analyzing the dynamics of a multi-agent learning system.