# Scheduling Jobs with Stochastic Holding Costs

arXiv: https://arxiv.org/abs/2105.13655 · HTML: https://mlsanity.com/paper/2105.13655/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 19 references that are in the map.
- First posted on arXiv 28 May 2021.

## Builds on (most cited first, 4 of 4)

- [Introduction to Multi-Armed Bandits](https://mlsanity.com/paper/1904.07272/) (2019)
- [Learning Scheduling Algorithms for Data Processing Clusters](https://mlsanity.com/paper/1810.01963/) (2018)
- [Convex Relaxations for Permutation Problems](https://mlsanity.com/paper/1306.4805/) (2013)
- [On Learning the cμ Rule in Single and Parallel Server Networks](https://mlsanity.com/paper/1802.06723/) (2018)

## Built on by (most cited first, 1 of 1)

- [On Preemption and Learning in Stochastic Scheduling](https://mlsanity.com/paper/2205.15695/) (2022)

## Abstract (arXiv)

We study a single-server scheduling problem for the objective of minimizing the expected cumulative holding cost incurred by jobs, where parameters defining stochastic job holding costs are unknown to the scheduler. We consider a general setting allowing for different job classes, where jobs of the same class have statistically identical holding costs and service times, with an arbitrary number of jobs across classes. In each time step, the server can process a job and observes random holding costs of the jobs that are yet to be completed. We consider a learning-based cμ rule scheduling which starts with a preemption period of fixed duration, serving as a learning phase, and having gathered data about jobs, it switches to nonpreemptive scheduling. Our algorithms are designed to handle instances with large and small gaps in mean job holding costs and achieve near-optimal performance guarantees. The performance of algorithms is evaluated by regret, where the benchmark is the minimum possible total holding cost attained by the cμ rule scheduling policy when the parameters of jobs are known. We show regret lower bounds and algorithms that achieve nearly matching regret upper bounds. Our numerical results demonstrate the efficacy of our algorithms and show that our regret analysis is nearly tight.