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Sion's Minimax Theorem in Geodesic Metric Spaces and a Riemannian Extragradient Algorithm
Peiyuan Zhang, Jingzhao Zhang, Suvrit Sra
Deciding whether saddle points exist or are approximable for nonconvex-nonconcave problems is usually intractable. This paper takes a step towards understanding a broad class of no…
Rethinking the Variational Interpretation of Nesterov's Accelerated Method
Peiyuan Zhang, Antonio Orvieto, Hadi Daneshmand
The continuous-time model of Nesterov's momentum provides a thought-provoking perspective for understanding the nature of the acceleration phenomenon in convex optimization. One of…
Revisiting the Role of Euler Numerical Integration on Acceleration and Stability in Convex Optimization
Peiyuan Zhang, Antonio Orvieto, Hadi Daneshmand +2
Viewing optimization methods as numerical integrators for ordinary differential equations (ODEs) provides a thought-provoking modern framework for studying accelerated first-order…