10 papers
Small Gradient Norm Regret for Online Convex Optimization
Wenzhi Gao, Chang He, Madeleine Udell
This paper introduces a new problem-dependent regret measure for online convex optimization with smooth losses. The notion, which we call the regret, depends on the cumul…
A Smooth Approximation Framework for Weakly Convex Optimization
Qi Deng, Wenzhi Gao
Standard complexity analyses for weakly convex optimization rely on the Moreau envelope technique proposed by Davis and Drusvyatskiy (2019). The main insight is that nonsmooth algo…
New Results on the Polyak Stepsize: Tight Convergence Analysis and Universal Function Classes
Chang He, Wenzhi Gao, Bo Jiang +2
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 convergenc…
Gradient Methods with Online Scaling Part II. Practical Aspects
Ya-Chi Chu, Wenzhi Gao, Yinyu Ye +1
Part I of this work [Gao25] establishes online scaled gradient methods (OSGM), a framework that utilizes online convex optimization to adapt stepsizes in gradient methods. This pap…
Gradient Methods with Online Scaling Part I. Theoretical Foundations
Wenzhi Gao, Ya-Chi Chu, Yinyu Ye +1
This paper establishes the theoretical foundations of the online scaled gradient methods (OSGM), a framework that utilizes online learning to adapt stepsizes and provably accelerat…
Provable and Practical Online Learning Rate Adaptation with Hypergradient Descent
Ya-Chi Chu, Wenzhi Gao, Yinyu Ye +1
This paper investigates the convergence properties of the hypergradient descent method (HDM), a 25-year-old heuristic originally proposed for adaptive stepsize selection in stochas…