A Variational Perspective on High-Resolution ODEs
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In this talk, we consider unconstrained minimization of smooth convex functions. A variational perspective on high-resolution ODEs using forced Euler-Lagrange equation is proposed. Our study results in a faster convergence rate for gradient norm minimization using Nesterov’s accelerated gradient method. We show that rate-matching discretization technique implicitly perturbs. Furthermore, we propose a stochastic method for noisy gradients.