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Stochastic Non-convex Optimization with Strong High Probability Second-order Convergence (1710.09447v2)

Published 25 Oct 2017 in math.OC, cs.LG, and stat.ML

Abstract: In this paper, we study stochastic non-convex optimization with non-convex random functions. Recent studies on non-convex optimization revolve around establishing second-order convergence, i.e., converging to a nearly second-order optimal stationary points. However, existing results on stochastic non-convex optimization are limited, especially with a high probability second-order convergence. We propose a novel updating step (named NCG-S) by leveraging a stochastic gradient and a noisy negative curvature of a stochastic Hessian, where the stochastic gradient and Hessian are based on a proper mini-batch of random functions. Building on this step, we develop two algorithms and establish their high probability second-order convergence. To the best of our knowledge, the proposed stochastic algorithms are the first with a second-order convergence in {\it high probability} and a time complexity that is {\it almost linear} in the problem's dimensionality.

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Authors (2)
  1. Mingrui Liu (44 papers)
  2. Tianbao Yang (162 papers)
Citations (3)

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