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• W2781023512 abstract "We propose stochastic optimization algorithms that can find local minima faster than existing algorithms for nonconvex optimization problems, by exploiting the third-order smoothness to escape non-degenerate saddle points more efficiently. More specifically, the proposed algorithm only needs $tilde{O}(epsilon^{-10/3})$ stochastic gradient evaluations to converge to an approximate local minimum $mathbf{x}$, which satisfies $|nabla f(mathbf{x})|_2leqepsilon$ and $lambda_{min}(nabla^2 f(mathbf{x}))geq -sqrt{epsilon}$ in the general stochastic optimization setting, where $tilde{O}(cdot)$ hides logarithm polynomial terms and constants. This improves upon the $tilde{O}(epsilon^{-7/2})$ gradient complexity achieved by the state-of-the-art stochastic local minima finding algorithms by a factor of $tilde{O}(epsilon^{-1/6})$. For nonconvex finite-sum optimization, our algorithm also outperforms the best known algorithms in a certain regime." @default.
• W2781023512 created "2018-01-05" @default.
• W2781023512 creator A5051448391 @default.
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• W2781023512 date "2017-12-18" @default.
• W2781023512 modified "2023-09-23" @default.
• W2781023512 title "Third-order Smoothness Helps: Even Faster Stochastic Optimization Algorithms for Finding Local Minima" @default.
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