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- W2808489849 abstract "Stochastic gradient descent (SGD) gives an optimal convergence rate when minimizing convex stochastic objectives $f(x)$. However, in terms of making the gradients small, the original SGD does not give an optimal rate, even when $f(x)$ is convex. If $f(x)$ is convex, to find a point with gradient norm $varepsilon$, we design an algorithm SGD3 with a near-optimal rate $tilde{O}(varepsilon^{-2})$, improving the best known rate $O(varepsilon^{-8/3})$. If $f(x)$ is nonconvex, to find its $varepsilon$-approximate local minimum, we design an algorithm SGD5 with rate $tilde{O}(varepsilon^{-3.5})$, where previously SGD variants only achieve $tilde{O}(varepsilon^{-4})$. This is no slower than the best known stochastic version of Newton's method in all parameter regimes." @default.
- W2808489849 created "2018-06-21" @default.
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- W2808489849 date "2018-12-02" @default.
- W2808489849 modified "2023-09-24" @default.
- W2808489849 title "How To Make the Gradients Small Stochastically: Even Faster Convex and Nonconvex SGD" @default.
- W2808489849 hasPublicationYear "2018" @default.
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