A Hitting Time Analysis of Stochastic Gradient Langevin Dynamics

@inproceedings{Zhang2017AHT,
  title={A Hitting Time Analysis of Stochastic Gradient Langevin Dynamics},
  author={Yuchen Zhang and Percy Liang and Moses Charikar},
  booktitle={COLT},
  year={2017}
}
We study the Stochastic Gradient Langevin Dynamics (SGLD) algorithm for non-convex optimization. The algorithm performs a stochastic gradient descent, where in each step it injects appropriately scaled Gaussian noise to the update. We analyze the algorithm’s hitting time to an arbitrary subset of the parameter space. Two results follow from our general theory: First, we prove that for empirical risk minimization, if the empirical risk is point-wise close to the (smooth) population risk, then… CONTINUE READING
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Guarantees in wasserstein distance for the langevin monte carlo algorithm

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