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Poster
Adaptive Stochastic Variance Reduction for Non-convex Finite-Sum Minimization
Ali Kavis · Stratis Skoulakis · Kimon Antonakopoulos · Leello Tadesse Dadi · Volkan Cevher

Thu Dec 01 02:00 PM -- 04:00 PM (PST) @ Hall J #816
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), but a fairly distinct, adaptive step-size schedule with the recursive \textit{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.