Adaptive Stochastic Variance Reduction for Non-convex Finite-Sum Minimization

TL;DR

AdaSpider is a novel adaptive variance-reduction algorithm for non-convex finite-sum optimization that does not require prior knowledge of problem parameters and achieves optimal oracle complexity.

Contribution

It introduces AdaSpider, the first parameter-free non-convex variance-reduction method with optimal complexity bounds.

Findings

Achieves $ ilde{O}(n + rac{ oot{n}}{ ext{epsilon}^2})$ oracle calls for $ ext{epsilon}$-stationary points.

Does not require knowledge of smoothness constant, target accuracy, or gradient bounds.

Matches the lower bound complexity up to logarithmic factors.

Abstract

We propose an adaptive variance-reduction method, called AdaSpider, for minimization of $L$-smooth, non-convex functions with a finite-sum structure. In essence, AdaSpider combines an AdaGrad-inspired [Duchi et al., 2011, McMahan & Streeter, 2010], but a fairly distinct, adaptive step-size schedule with the recursive stochastic path integrated estimator proposed in [Fang et al., 2018]. To our knowledge, Adaspider is the first parameter-free non-convex variance-reduction method in the sense that it does not require the knowledge of problem-dependent parameters, such as smoothness constant $L$, target accuracy $\epsilon$ or any bound on gradient norms. In doing so, we are able to compute an $\epsilon$-stationary point with $\tilde{O}\left(n + \sqrt{n}/\epsilon^2\right)$ oracle-calls, which matches the respective lower bound up to logarithmic factors.