  We consider the problem of scheduling in constrained queueing networks with a
view to minimizing packet delay. Modern communication systems are becoming
increasingly complex, and are required to handle multiple types of traffic with
widely varying characteristics such as arrival rates and service times. This,
coupled with the need for rapid network deployment, render a bottom up approach
of first characterizing the traffic and then devising an appropriate scheduling
protocol infeasible.
  In contrast, we formulate a top down approach to scheduling where, given an
unknown network and a set of scheduling policies, we use a policy gradient
based reinforcement learning algorithm that produces a scheduler that performs
better than the available atomic policies. We derive convergence results and
analyze finite time performance of the algorithm. Simulation results show that
the algorithm performs well even when the arrival rates are nonstationary and
can stabilize the system even when the constituent policies are unstable.
