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arXiv · 2202.04598

Reproducibility in Optimization: Theoretical Framework and Limits

Kwangjun Ahn·Prateek Jain·Ziwei Ji·Satyen Kale·Praneeth Netrapalli·Gil I. Shamir
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Abstract

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.

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Kwangjun Ahn, Prateek Jain, Ziwei Ji, Satyen Kale, Praneeth Netrapalli, Gil I. Shamir. 2022-02-09. Reproducibility in Optimization: Theoretical Framework and Limits. https://arxiv.org/abs/2202.04598

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