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    Momentum-Based Variance Reduction in Non-Convex SGD

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    Variance reduction has emerged in recent years as a strong competitor to stochastic gradient descent in non-convex problems, providing the first algorithms to improve upon the converge rate of stochastic gradient descent for finding first-order critical points. However, variance reduction techniques typically require carefully tuned learning rates and willingness to use excessively large "mega-batches" in order to achieve their improved results. We present a new algorithm, STORM, that does not require any batches and makes use of adaptive learning rates, enabling simpler implementation and less hyperparameter tuning. Our technique for removing the batches uses a variant of momentum to achieve variance reduction in non-convex optimization. On smooth losses FF, STORM finds a point x\boldsymbol{x} with E[F(x)]O(1/T+σ1/3/T1/3)\mathbb{E}[\|\nabla F(\boldsymbol{x})\|]\le O(1/\sqrt{T}+\sigma^{1/3}/T^{1/3}) in TT iterations with σ2\sigma^2 variance in the gradients, matching the optimal rate but without requiring knowledge of σ\sigma.Comment: Added Ac

    Momentum-based variance reduction in non-convex SGD

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    Variance reduction has emerged in recent years as a strong competitor to stochastic gradient descent in non-convex problems, providing the first algorithms to improve upon the converge rate of stochastic gradient descent for finding first-order critical points. However, variance reduction techniques typically require carefully tuned learning rates and willingness to use excessively large “mega-batches” in order to achieve their improved results. We present a new algorithm, Storm, that does not require any batches and makes use of adaptive learning rates, enabling simpler implementation and less hyperparameter tuning. Our technique for removing the batches uses a variant of momentum to achieve variance reduction in non-convex optimization. On smooth losses F, Storm finds a point x with E[k∇F(x)k] ≤ O(1 /√ T + σ^1/3 /T^1/3) in T iterations with σ^2 variance in the gradients, matching the optimal rate and without requiring knowledge of σ.https://arxiv.org/pdf/1905.10018.pdfPublished versio
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