In this paper, we revisit a classical adaptive stepsize strategy for gradient descent: the Polyak stepsize (PolyakGD), originally proposed in Polyak (1969). We study the convergence behavior of PolyakGD from two perspectives: tight worst-case analysis and universality across function classes. As our first main result, we establish the tightness of the known convergence rates of … Read more
This paper establishes the theoretical foundations of the online scaled gradient methods (OSGM), a framework that utilizes online learning to adapt stepsizes and provably accelerate first-order methods. OSGM quantifies the effectiveness of a stepsize by a feedback function motivated from a convergence measure and uses the feedback to adjust the stepsize through an online learning … Read more
A pruning-aware adaptive gradient method is proposed which classifies the variables in two sets before updating them using different strategies. This technique extends the “relevant/irrelevant” approach of Ding (2019) and Zimmer et al. (2022) and allows a posteriori sparsification of the solution of model parameter fitting problems. The new method is proved to be convergent … Read more