Focus Period Lund 2026
PhD Student
University of Pennsylvania (USA)
Henry Shugart is a third-year Ph.D. student in the Wharton Department of Statistics and Data Science at the University of Pennsylvania, advised by Prof. Jason Altschuler. His research interests lie broadly in optimization and machine learning, with a particular focus on min-max problems. Previously Henry earned his undergraduate degree from the University of North Carolina at Chapel Hill, where he majored in statistics and analytics, as well as mathematics.
Presenting: Negative Stepsizes Make Gradient-Descent-Ascent Converge
Solving min-max problems is a central question in optimization, games, learning, and controls. Arguably the most natural algorithm is Gradient-Descent-Ascent (GDA), however since the 1970s, conventional wisdom has argued that it fails toconverge even on simple problems. This failure spurred the extensive literature on modifying GDA with extragradients, optimism, momentum, anchoring, etc. In contrast, we show that GDA converges in its original form by simply using a judicious choice of stepsizes. The key innovation is the proposal of unconventional stepsize schedules that are time-varying, asymmetric, and (most surprisingly) periodically negative. We show that all three properties are necessary for convergence, and that altogether this enables GDA to converge on the classical counterexamples (e.g., unconstrained convex-concave problems). The core intuition is that although negative stepsizes make backward progress, they de-synchronize the min/max variables (overcoming the cycling issue of GDA) and lead to a slingshot phenomenon in which the forward progress in the other iterations is overwhelmingly larger. This results in fast overall convergence. Geometrically, the slingshot dynamics leverage the non-reversibility of gradient flow: positive/negative steps cancel to first order, yielding a second-order net movement in a new direction that leads to convergence and is otherwise impossible for GDA to movein. Joint work with Jason Altschuler.