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