Reproducibility in Optimization: Theoretical Framework and Limits

TL;DR

This paper develops a formal framework to quantify and analyze the limits of reproducibility in optimization procedures, revealing a fundamental trade-off between computational effort and reproducibility in various convex settings.

Contribution

It introduces a quantitative measure of reproducibility and establishes tight bounds on its limits across different convex optimization scenarios.

Findings

Reproducibility bounds vary across convex optimization types.

More computation improves reproducibility, indicating a trade-off.

The framework formalizes reproducibility in noisy or error-prone optimization contexts.

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.