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math.OC2019
No-collision Transportation Maps
Levon Nurbekyan, Alexander Iannantuono, Adam M. Oberman
Transportation maps between probability measures are critical objects in numerous areas of mathematics and applications such as PDE, fluid mechanics, geometry, machine learning, co…
math.OC2019
Nesterov's method with decreasing learning rate leads to accelerated stochastic gradient descent
Maxime Laborde, Adam M. Oberman
We present a coupled system of ODEs which, when discretized with a constant time step/learning rate, recovers Nesterov's accelerated gradient descent algorithm. The same ODEs, when…
math.OC2019★ 7 cited
Stochastic Gradient Descent with Polyak's Learning Rate
Adam M. Oberman, Mariana Prazeres
Stochastic gradient descent (SGD) for strongly convex functions converges at the rate $\bO(1/k)$. However, achieving good results in practice requires tuning the parameters (for ex…