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

Marten van Dijk · Lam Nguyen · PHUONG_HA NGUYEN · Dzung Phan

Pacific Ballroom #193

Keywords: [ Convex Optimization ]


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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