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

• URL: http://arxiv.org/abs/2211.01851v1
• Date: Thu, 3 Nov 2022 14:41:46 GMT
• Title: Adaptive Stochastic Variance Reduction for Non-convex Finite-Sum Minimization
• Authors: Ali Kavis, Stratis Skoulakis, Kimon Antonakopoulos, Leello Tadesse Dadi, Volkan Cevher
• Abstract summary: We propose an adaptive variance method, called AdaSpider, for $L$-smooth, non-reduction functions with a finitesum structure. In doing so, we are able to compute an $epsilon-stationary point with $tildeOleft + st/epsilon calls.
• Score: 52.25843977506935
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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