NEON2: Finding Local Minima via First-Order Oracles

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

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Zeyuan Allen-Zhu, Yuanzhi Li


We propose a reduction for non-convex optimization that can (1) turn an stationary-point finding algorithm into an local-minimum finding one, and (2) replace the Hessian-vector product computations with only gradient computations. It works both in the stochastic and the deterministic settings, without hurting the algorithm's performance.

As applications, our reduction turns Natasha2 into a first-order method without hurting its theoretical performance. It also converts SGD, GD, SCSG, and SVRG into algorithms finding approximate local minima, outperforming some best known results.