A Hitting Time Analysis of Stochastic Gradient Langevin Dynamics
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Proceedings of the 2017 Conference on Learning Theory, PMLR 65:19802022, 2017.
Abstract
We study the Stochastic Gradient Langevin Dynamics (SGLD) algorithm for nonconvex optimization. The algorithm performs 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 pointwise close to the (smooth) population risk, then the algorithm achieves an approximate local minimum of the population risk in polynomial time, escaping suboptimal local minima that only exist in the empirical risk. Second, we show that SGLD improves on one of the best known learnability results for learning linear classifiers under the zeroone loss.
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