Cloud providers rent out surplus computational resources as spot instances at a deep discount. However, these cheap spot instances are revocable. When demand surges for higher priced on-demand instances, cloud providers can interrupt these spot instances after a brief alert. Such unreliability makes it challenging to utilize spot instances for many long-running jobs. However, with checkpoints and restoration, machine-learning (ML) training jobs are a good candidate to overcome this difficulty. In this paper, we formalize the problem of scheduling ML-training jobs on transient spot instances, especially from an ML researcher's view, who may have some grant/credit for renting cloud computing services for several ML training tasks. Such a researcher would need to partition the computational resources wisely to maximize outcome (or total expected utility of all jobs) while maintaining some fairness between jobs. We investigate the trade-off between low-cost/interruptible and high-cost/uninterruptible computation, by proposing a linear-programming (LP) rounding based polynomial time algorithm. Based on the LP solution, we also give an LP-based heuristic that performs well in practice. We implement and evaluate these algorithms, and are able to achieve the same utility with 23% to 48% of the budget needed with on-demand instances. Moreover, the total utility we get is close to the theoretical upper bound under various settings, indicating close to optimal performance.