# Nonasymptotic estimates for Stochastic Gradient Langevin Dynamics under local conditions in nonconvex optimization

Ying Zhang, Ömer Deniz Akyildiz, Theo Damoulas, Sotirios Sabanis

Research output: Working paper

## Abstract

Within the context of empirical risk minimization, see Raginsky, Rakhlin, and Telgarsky (2017), we are concerned with a non-asymptotic analysis of sampling algorithms used in optimization. In particular, we obtain non-asymptotic error bounds for a popular class of algorithms called Stochastic Gradient Langevin Dynamics (SGLD). These results are derived in appropriate Wasserstein distances in the absence of the log-concavity of the target distribution. More precisely, the local Lipschitzness of the stochastic gradient $H(\theta, x)$ is assumed, and furthermore, the dissipativity and convexity at infinity condition are relaxed by removing the uniform dependence in $x$.
Original language English ArXiv Published - 4 Oct 2019

• math.ST
• cs.LG
• math.PR
• stat.ML
• stat.TH
• 65C40, 62L10

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