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Poster
On the Convergence of Nesterov's Accelerated Gradient Method in Stochastic Settings
Mahmoud Assran · Michael Rabbat

Wed Jul 15 05:00 AM -- 05:45 AM & Wed Jul 15 04:00 PM -- 04:45 PM (PDT) @
in Poster Session 21 »

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.

Keywords: Convex Optimization · Optimization - Convex

Author Information

Mahmoud Assran (McGill University; Mila; Facebook AI Research)
Michael Rabbat (Facebook)

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