Online Adaptive Methods, Universality and Acceleration

Part of Advances in Neural Information Processing Systems 31 (NeurIPS 2018)

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Kfir Y. Levy, Alp Yurtsever, Volkan Cevher


<p>We present a novel method for convex unconstrained optimization that, without any modifications ensures: (1) accelerated convergence rate for smooth objectives, (2) standard convergence rate in the general (non-smooth) setting, and (3) standard convergence rate in the stochastic optimization setting. <br /> To the best of our knowledge, this is the first method that simultaneously applies to all of the above settings. <br /> At the heart of our method is an adaptive learning rate rule that employs importance weights, in the spirit of adaptive online learning algorithms [duchi2011adaptive,levy2017online], combined with an update that linearly couples two sequences, in the spirit of [AllenOrecchia2017]. An empirical examination of our method demonstrates its applicability to the above mentioned scenarios and corroborates our theoretical findings.</p>