Online Task Scheduling and Termination With Throughput Constraint

We consider the task scheduling scenario where the controller activates one from
$K$
task types at each time. Each task induces a random completion time, and a reward is obtained only after the task is completed. The statistics of the completion time and the reward distributions of all task types are unknown to the controller. The controller needs to learn to schedule tasks to maximize the accumulated reward within a given time horizon
$T$
. Motivated by the practical scenarios, we require the designed policy to satisfy a system throughput constraint. In addition, we introduce the interruption mechanism to terminate ongoing tasks that last longer than certain deadlines. To address this scheduling problem, we model it as an online learning problem with deadline and throughput constraints. Then, we characterize the optimal offline policy and develop efficient online learning algorithms based on the Lyapunov method. We prove that our online learning algorithm achieves an
$O(\sqrt{T})$
regret and zero constraint violation. We also conduct simulations to evaluate the performance of our developed learning algorithms.