Max Weight Learning Algorithms for Scheduling in Unknown Environments

We consider a discrete time queueing system where a controller makes a 2-stage decision every slot. The decision at the first stage reveals a hidden source of randomness with a control-dependent (but unknown) probability distribution. The decision at the second stage generates an attribute vector that depends on this revealed randomness. The goal is to stabilize all queues and optimize a utility function of time average attributes, subject to an additional set of time average constraints. This setting fits a wide class of stochastic optimization problems, including multi-user wireless scheduling with dynamic channel measurement decisions, and wireless multi-hop routing with multi-receiver diversity and opportunistic routing decisions. We develop a simple max-weight algorithm that learns efficient behavior by averaging functionals of previous outcomes.