Stability and Generalization for Randomized Coordinate Descent

TL;DR

This paper introduces the first stability-based generalization analysis for randomized coordinate descent (RCD), demonstrating its superior stability over stochastic gradient descent and providing guidelines for early stopping to optimize generalization.

Contribution

It pioneers the stability analysis of RCD for convex and strongly convex objectives, linking stability to generalization bounds and early stopping strategies.

Findings

RCD has better stability than stochastic gradient descent.

Optimal early stopping can improve generalization.

Provides theoretical bounds for RCD's generalization performance.

Abstract

Randomized coordinate descent (RCD) is a popular optimization algorithm with wide applications in solving various machine learning problems, which motivates a lot of theoretical analysis on its convergence behavior. As a comparison, there is no work studying how the models trained by RCD would generalize to test examples. In this paper, we initialize the generalization analysis of RCD by leveraging the powerful tool of algorithmic stability. We establish argument stability bounds of RCD for both convex and strongly convex objectives, from which we develop optimal generalization bounds by showing how to early-stop the algorithm to tradeoff the estimation and optimization. Our analysis shows that RCD enjoys better stability as compared to stochastic gradient descent.