Reproducibility in Optimization: Theoretical Framework and Limits

Part of Advances in Neural Information Processing Systems 35 (NeurIPS 2022) Main Conference Track

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Kwangjun Ahn, Prateek Jain, Ziwei Ji, Satyen Kale, Praneeth Netrapalli, Gil I Shamir


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.