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Found 7 papers, 0 papers with code
Stochastic Modified Flows for Riemannian Stochastic Gradient Descent
We give quantitative estimates for the rate of convergence of Riemannian stochastic gradient descent (RSGD) to Riemannian gradient flow and to a diffusion process, the so-called Riemannian stochastic modified flow (RSMF).
Stochastic Modified Flows, Mean-Field Limits and Dynamics of Stochastic Gradient Descent
We propose new limiting dynamics for stochastic gradient descent in the small learning rate regime called stochastic modified flows.
Convergence rates for momentum stochastic gradient descent with noise of machine learning type
We consider the momentum stochastic gradient descent scheme (MSGD) and its continuous-in-time counterpart in the context of non-convex optimization.
Conservative SPDEs as fluctuating mean field limits of stochastic gradient descent
The convergence of stochastic interacting particle systems in the mean-field limit to solutions of conservative stochastic partial differential equations is established, with optimal rate of convergence.
Numerical approximation of singular-degenerate parabolic stochastic PDEs
We study a general class of singular degenerate parabolic stochastic partial differential equations (SPDEs) which include, in particular, the stochastic porous medium equations and the stochastic fast diffusion equation.
Numerical Analysis Numerical Analysis
Conservative stochastic PDE and fluctuations of the symmetric simple exclusion process
In the small-noise limit, we show that the fluctuations of the solutions are to first-order the same as the fluctuations of the particle system.
Probability Analysis of PDEs
Convergence rates for the stochastic gradient descent method for non-convex objective functions
We prove the local convergence to minima and estimates on the rate of convergence for the stochastic gradient descent method in the case of not necessarily globally convex nor contracting objective functions.
