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.

翻译：我们开始正式研究优化中的可复制性。 我们定义了在面临不精确或随机梯度计算或不精确初始化等噪音或易出错操作的情况下优化程序的可复制性的数量尺度。 然后我们分析了一些利益上的二次曲线优化设置, 如平滑、非平滑和强通的客观功能, 并对每个环境的可复制性限制设定了严格的界限。 我们的分析揭示了计算和可复制之间的根本权衡: 更多的计算对于更好的可复制性是必要的( 并且足够 ) 。