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Activity Number: 202 - Monte Carlo Methods and Simulation I
Type: Contributed
Date/Time: Tuesday, August 4, 2020 : 10:00 AM to 2:00 PM
Sponsor: Section on Statistical Computing
Abstract #313913
Title: Sampling and Optimization Analysis for SGD and LMC
Author(s): Riddhiman Bhattacharya*
Companies: University of Minnesota
Keywords: SGD; LMC; Langevin Equation; sampling; optimization
Abstract:

We study the Langevin Monte Carlo(LMC) and Stochastic Gradient Descent(SGD) algoithms with the LMC in both the overdamped and underdamped cases. We prove that the SGD algorithm behaves as a diffusion when the step size is small. The error in this approximation is the order of the step size. We define the perturbed SGD and LMC algorithms. We obtain diffusion limits of both the perturbed SGD and LMC in terms of the first moment. We also show that the LMC converges and find rates for the convergence of LMC.


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