Sojourn Time Minimization of Successful Jobs

Due to a growing interest in deep learning applications [5], compute-intensive and long-running (hours to days) training jobs have become a significant component of datacenter workloads. A large fraction of these jobs is often exploratory, with the goal of determining the best model structure (e.g., the number of layers and channels in a convolutional neural network), hyperparameters (e.g., the learning rate), and data augmentation strategies for the target application. Notably, training jobs are often terminated early if their learning metrics (e.g., training and validation accuracy) are not converging, with only a few completing successfully. For this motivating application, we consider the problem of scheduling a set of jobs that can be terminated at predetermined checkpoints with known probabilities estimated from historical data. We prove that, in order to minimize the time to complete the first K successful jobs on a single server, optimal scheduling does not require preemption (even when preemption overhead is negligible) and provide an optimal policy; advantages of this policy are quantified through simulation. Related Work. While job scheduling has been investigated extensively in many scenarios (see [6] and [2] for a survey of recent result), most policies require that the cost of waiting times of each job be known at scheduling time; in contrast, in our setting the scheduler does not know which job will be the K-th successful job, and sojourn times of subsequent jobs do not contribute to the target metric. For example, [4, 3] minimize makespan (i.e., the time to complete all jobs) for known execution times and waiting time costs; similarly, Gittins index [1] and SR rank [7] minimize expected sojourn time of all jobs, i.e., both successfully completed jobs and jobs terminated early. Unfortunately, scheduling policies not distinguishing between these two types of jobs may favor jobs where the next stage is short and leads to early termination with high probability, which is an undesirable outcome in our applications of interest.