Reproducibility in Optimization: Theoretical Framework and Limits
This addresses reproducibility issues for researchers and practitioners in optimization, providing a foundational theoretical framework.
The paper tackles the problem of reproducibility in optimization by defining a quantitative measure and analyzing limits for various convex settings, revealing a fundamental trade-off where more computation is necessary and sufficient for better reproducibility.
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.