Accelerated Gradient Flow: Risk, Stability, and Implicit Regularization
This addresses the gap in understanding implicit regularization for accelerated methods, which are standard in ML, but the work is incremental as it builds on prior analyses of unaccelerated methods.
The paper tackles the statistical risk of accelerated gradient methods (Nesterov's and Polyak's) in least squares regression, revealing connections to explicit penalization and complex interactions between early stopping, stability, and loss curvature through sharper continuous-time analyses.
Acceleration and momentum are the de facto standard in modern applications of machine learning and optimization, yet the bulk of the work on implicit regularization focuses instead on unaccelerated methods. In this paper, we study the statistical risk of the iterates generated by Nesterov's accelerated gradient method and Polyak's heavy ball method, when applied to least squares regression, drawing several connections to explicit penalization. We carry out our analyses in continuous-time, allowing us to make sharper statements than in prior work, and revealing complex interactions between early stopping, stability, and the curvature of the loss function.