Confidence Intervals for the Interquartile Mean

Alexandra Burushkina, Philip S. Thomas; 7, 2026.

Presented at the Reinforcement Learning Conference (RLC), Montréal, Quebec, Canada, August 15–17, 2026.

Abstract

The interquartile mean (IQM) is increasingly used for evaluating reinforcement learning (RL) algorithms and is typically reported with confidence intervals. Despite its widespread use in RL, the IQM is still generally discussed as a sample statistic (like the sample mean), rather than as a parameter of a distribution (like the mean). We present a definition of the IQM as a parameter of a distribution and justify this definition. In RL, researchers typically use the percentile bootstrap method to obtain confidence intervals for the IQM. However, percentile bootstrap confidence intervals lack guaranteed coverage, meaning that these intervals may fail to contain the IQM more often than expected. As our primary contribution, we derive confidence intervals for the IQM that have guaranteed coverage, which, to our knowledge, is not provided by previous methods.

[abs][pdf]

BibTeX

@article{burushkina2026confidence,
    title={Confidence Intervals for the Interquartile Mean},
    author={Alexandra Burushkina and Philip S. Thomas},
    journal={Reinforcement Learning Journal},
    volume={7},
    pages={},
    year={2026}
}