On the Convergence of Nesterov's Accelerated Gradient Method in Stochastic Settings
By Mahmoud Assran, Michael G. Rabbat. 2020
74 citations recorded by the source corpus.
We study Nesterov's accelerated gradient method with constant step-size and momentum parameters in the stochastic approximation setting (unbiased gradients with bounded variance) and the finite-sum setting (where randomness is due to sampling mini-batches). To build better insight into the behavior of Nesterov's method in stochastic settings, we focus throughout on objectives that are smooth, strongly-convex, and twice continuously differentiable. In the stochastic approximation setting, Nesterov's method converges to a neighborhood of the optimal point at the same accelerated rate as in the deterministic setting. Perhaps surprisingly, in the finite-sum setting, we prove that Nesterov's method may diverge with the usual choice of step-size and momentum, unless additional conditions on the problem related to conditioning and data coherence are satisfied. Our results shed light as to why Nesterov's method may fail to converge or achieve acceleration in the finite-sum setting.
Subfields: Optimization & Training
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In Optimization & Training
- Nicolas Loizou
- Simon Lacoste-Julien
- Ioannis Mitliagkas
- Hugo Berard
- Pascal Vincent
- Peter Richtárik
- Alexia Jolicoeur-Martineau
- Gauthier Gidel
Citations in the corpus
- Stochastic Hamiltonian Gradient Methods for Smooth Games (2020, methodology): “A natural extension of our results will be the proposal of accelerated Hamiltonian methods that use momentum (Loizou & Richt´arik, 2017; Assran & Rabbat, 2020) on top of the Hamiltonian gradient update.”