The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Jason D Lee - One of the best experts on this subject based on the ideXlab platform.
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stochastic subgradient Method Converges on tame functions
Foundations of Computational Mathematics, 2020Co-Authors: Damek Davis, Dmitriy Drusvyatskiy, Sham M Kakade, Jason D LeeAbstract:This work considers the question: what convergence guarantees does the stochastic subgradient Method have in the absence of smoothness and convexity? We prove that the stochastic subgradient Method, on any semialgebraic locally Lipschitz function, produces limit points that are all first-order stationary. More generally, our result applies to any function with a Whitney stratifiable graph. In particular, this work endows the stochastic subgradient Method, and its proximal extension, with rigorous convergence guarantees for a wide class of problems arising in data science—including all popular deep learning architectures.
Damek Davis - One of the best experts on this subject based on the ideXlab platform.
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stochastic subgradient Method Converges on tame functions
Foundations of Computational Mathematics, 2020Co-Authors: Damek Davis, Dmitriy Drusvyatskiy, Sham M Kakade, Jason D LeeAbstract:This work considers the question: what convergence guarantees does the stochastic subgradient Method have in the absence of smoothness and convexity? We prove that the stochastic subgradient Method, on any semialgebraic locally Lipschitz function, produces limit points that are all first-order stationary. More generally, our result applies to any function with a Whitney stratifiable graph. In particular, this work endows the stochastic subgradient Method, and its proximal extension, with rigorous convergence guarantees for a wide class of problems arising in data science—including all popular deep learning architectures.
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stochastic subgradient Method Converges at the rate o k 1 4 on weakly convex functions
arXiv: Optimization and Control, 2018Co-Authors: Damek Davis, Dmitriy DrusvyatskiyAbstract:We prove that the projected stochastic subgradient Method, applied to a weakly convex problem, drives the gradient of the Moreau envelope to zero at the rate $O(k^{-1/4})$.
Fredrik Lindgren - One of the best experts on this subject based on the ideXlab platform.
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on the backward euler approximation of the stochastic allen cahn equation
Journal of Applied Probability, 2015Co-Authors: Mihaly Kovacs, Stig Larsson, Fredrik LindgrenAbstract:We consider the stochastic Allen-Cahn equation perturbed by smooth additive Gaussian noise in a spatial domain with smooth boundary in dimension d ≤ 3, and study the semidiscretization in time of the equation by an implicit Euler Method. We show that the Method Converges pathwise with a rate O(Δt^γ) for any γ < ½. We also prove that the scheme Converges uniformly in the strong L^p -sense but with no rate given.
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on the backward euler approximation of the stochastic allen cahn equation
arXiv: Numerical Analysis, 2013Co-Authors: Mihaly Kovacs, Stig Larsson, Fredrik LindgrenAbstract:We consider the stochastic Allen-Cahn equation perturbed by smooth additive Gaussian noise in a spatial domain with smooth boundary in dimension $d\le 3$, and study the semidiscretization in time of the equation by an implicit Euler Method. We show that the Method Converges pathwise with a rate $O(\Delta t^{\gamma}) $ for any $\gamma<\frac12$. We also prove that the scheme Converges uniformly in the strong $L^p$-sense but with no rate given.
Dmitriy Drusvyatskiy - One of the best experts on this subject based on the ideXlab platform.
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stochastic subgradient Method Converges on tame functions
Foundations of Computational Mathematics, 2020Co-Authors: Damek Davis, Dmitriy Drusvyatskiy, Sham M Kakade, Jason D LeeAbstract:This work considers the question: what convergence guarantees does the stochastic subgradient Method have in the absence of smoothness and convexity? We prove that the stochastic subgradient Method, on any semialgebraic locally Lipschitz function, produces limit points that are all first-order stationary. More generally, our result applies to any function with a Whitney stratifiable graph. In particular, this work endows the stochastic subgradient Method, and its proximal extension, with rigorous convergence guarantees for a wide class of problems arising in data science—including all popular deep learning architectures.
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stochastic subgradient Method Converges at the rate o k 1 4 on weakly convex functions
arXiv: Optimization and Control, 2018Co-Authors: Damek Davis, Dmitriy DrusvyatskiyAbstract:We prove that the projected stochastic subgradient Method, applied to a weakly convex problem, drives the gradient of the Moreau envelope to zero at the rate $O(k^{-1/4})$.
Mihaly Kovacs - One of the best experts on this subject based on the ideXlab platform.
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on the backward euler approximation of the stochastic allen cahn equation
Journal of Applied Probability, 2015Co-Authors: Mihaly Kovacs, Stig Larsson, Fredrik LindgrenAbstract:We consider the stochastic Allen-Cahn equation perturbed by smooth additive Gaussian noise in a spatial domain with smooth boundary in dimension d ≤ 3, and study the semidiscretization in time of the equation by an implicit Euler Method. We show that the Method Converges pathwise with a rate O(Δt^γ) for any γ < ½. We also prove that the scheme Converges uniformly in the strong L^p -sense but with no rate given.
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on the backward euler approximation of the stochastic allen cahn equation
arXiv: Numerical Analysis, 2013Co-Authors: Mihaly Kovacs, Stig Larsson, Fredrik LindgrenAbstract:We consider the stochastic Allen-Cahn equation perturbed by smooth additive Gaussian noise in a spatial domain with smooth boundary in dimension $d\le 3$, and study the semidiscretization in time of the equation by an implicit Euler Method. We show that the Method Converges pathwise with a rate $O(\Delta t^{\gamma}) $ for any $\gamma<\frac12$. We also prove that the scheme Converges uniformly in the strong $L^p$-sense but with no rate given.