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arXiv · 1810.04100

Characterization of Convex Objective Functions and Optimal Expected Convergence Rates for SGD

Marten van Dijk·Lam M. Nguyen·Phuong Ha Nguyen·Dzung T. Phan
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Abstract

We study Stochastic Gradient Descent (SGD) with diminishing step sizes for convex objective functions. We introduce a definitional framework and theory that defines and characterizes a core property, called curvature, of convex objective functions. In terms of curvature we can derive a new inequality that can be used to compute an optimal sequence of diminishing step sizes by solving a differential equation. Our exact solutions confirm known results in literature and allows us to fully characterize a new regularizer with its corresponding expected convergence rates.

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Marten van Dijk, Lam M. Nguyen, Phuong Ha Nguyen, Dzung T. Phan. 2018-10-09. Characterization of Convex Objective Functions and Optimal Expected Convergence Rates for SGD. https://arxiv.org/abs/1810.04100

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