4 papers
Negative Stepsizes Make Gradient-Descent-Ascent Converge
Henry Shugart, Jason M. Altschuler
Efficient computation of min-max problems is a central question in optimization, learning, games, and control. Arguably the most natural algorithm is gradient-descent-ascent (GDA).…
Acyclic Monotone Operators Are Not Closed Under Addition
Henry Shugart
Borwein and Wiersma [SIAM J. Optim. 18(3) (2007), 946-960] asked if the set of acyclic monotone operators is closed under addition. We answer this question in the negative.
Negative Momentum for Convex-Concave Optimization
Henry Shugart, Shuyi Wang, Jason M. Altschuler
This paper revisits momentum in the context of min-max optimization. Momentum is a celebrated mechanism for accelerating gradient dynamics in settings like convex minimization, but…
Min-Max Optimization Is Strictly Easier Than Variational Inequalities
Henry Shugart, Jason M. Altschuler
Classically, a mainstream approach for solving a convex-concave min-max problem is to instead solve the variational inequality problem arising from its first-order optimality condi…