Online Learning for Job Scheduling on Heterogeneous Machines

Motivated by the fair allocation of goods in an offline market, we propose and study a new model for online job scheduling on heterogeneous machines. In this model, the goal is to schedule jobs on a set of machines in an online fashion with the overall quality of service as close as possible to an optimal offline benchmark. More precisely, we consider a job scheduling system consisting of a set of machines and indivisible jobs that arrive sequentially over time. When a job arrives, it must be scheduled and processed on a single machine where the utility received for such an assignment depends on the job-machine pair. It is assumed that each machine has a different power/energy budget and its welfare is proportional to the product of its power and its cumulative utilities. The goal is to maximize the total quality of service that is the sum of all the machines' welfare. However, in practice, the power budgets of machines often are not known and must be learned over time. To tackle this issue, we first propose a simple Explore-then-Exploit scheduling algorithm that achieves a sub-linear regret of O(T-2/3), where T is the total number of jobs. Here the regret is defined as the expected difference between the total quality of service obtained by the algorithm and its maximum value had we known the power budgets a priori. We then enhance this result by providing an Upper Confidence Bound (UCB) algorithm with only logarithmic regret O(log T). Numerical results are conducted to evaluate the performance of the proposed algorithms for various ranges of parameters.