Papers › Non-convex Finite-Sum Optimization Via SCSG Methods
Non-convex Finite-Sum Optimization Via SCSG Methods
Lihua Lei, Cheng Ju, Jianbo Chen, Michael I. Jordan
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We develop a class of algorithms, as variants of the stochastically controlled stochastic gradient (SCSG) methods (Lei and Jordan, 2016), for the smooth non-convex finite-sum optimization problem. Assuming the smoothness of each component, the complexity of SCSG to reach a stationary point with 𝔼 ‖∇f(x)‖²≤ϵ is O(min{ϵ^(-5/3), ϵ⁻¹n^(2/3)}), which strictly outperforms the stochastic gradient descent. Moreover, SCSG is never worse than the state-of-the-art methods based on variance reduction and it significantly outperforms them when the target accuracy is low. A similar acceleration is also achieved when the functions satisfy the Polyak-Lojasiewicz condition. Empirical experiments demonstrate that SCSG outperforms stochastic gradient methods on training multi-layers neural networks in terms of both training and validation loss.
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