We initiate a formal study of reproducibility in optimization. We define a quantitative measure of reproducibility of optimization procedures in the face of noisy or error-prone operations such as inexact or stochastic gradient computations or inexact initialization. We then analyze several convex optimization settings of interest such as smooth, non-smooth, and strongly-convex objective functions and establish tight bounds on the limits of reproducibility in each setting. Our analysis reveals a fundamental trade-off between computation and reproducibility: more computation is necessary (and sufficient) for better reproducibility.
@article{arxiv.2202.04598,
title = {Reproducibility in Optimization: Theoretical Framework and Limits},
author = {Kwangjun Ahn and Prateek Jain and Ziwei Ji and Satyen Kale and Praneeth Netrapalli and Gil I. Shamir},
journal= {arXiv preprint arXiv:2202.04598},
year = {2022}
}