We examine the elastic scaling of Deep Learning (DL) jobs and propose a novel resource allocation strategy for DL training jobs, resulting in improved job run time performance as well as increased cluster utilization. We begin by analyzing DL workloads and exploit the fact that DL jobs can be run with a range of batch sizes without affecting their final accuracy. We formulate an optimization problem that explores a dynamic batch size allocation to individual DL jobs based on their scaling efficiency, when running on multiple nodes. We design a fast dynamic programming based optimizer to solve this problem in real-time to determine jobs that can be scaled up/down, and use this optimizer in an autoscaler to dynamically change the allocated resources and batch sizes of individual DL jobs. We demonstrate empirically that our elastic scaling algorithm can complete up to as many jobs as compared to a strong baseline algorithm that also scales the number of GPUs but does not change the batch size, with average completion times up to faster.