Stability and Generalization for Randomized Coordinate Descent
This work addresses the generalization performance of RCD for machine learning practitioners, providing theoretical insights into its stability compared to stochastic gradient descent, but it is incremental as it extends existing stability analysis to a new algorithm.
The paper tackles the lack of generalization analysis for models trained by randomized coordinate descent (RCD) by using algorithmic stability to derive stability bounds for convex and strongly convex objectives, resulting in optimal generalization bounds through early-stopping strategies.
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.