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arXiv · 1805.09416

Adaptive Stochastic Gradient Langevin Dynamics: Taming Convergence and Saddle Point Escape Time

Hejian Sang·Jia Liu
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Abstract

In this paper, we propose a new adaptive stochastic gradient Langevin dynamics (ASGLD) algorithmic framework and its two specialized versions, namely adaptive stochastic gradient (ASG) and adaptive gradient Langevin dynamics(AGLD), for non-convex optimization problems. All proposed algorithms can escape from saddle points with at most $O(\log d)$ iterations, which is nearly dimension-free. Further, we show that ASGLD and ASG converge to a local minimum with at most $O(\log d/\epsilon^4)$ iterations. Also, ASGLD with full gradients or ASGLD with a slowly linearly increasing batch size converge to a local minimum with iterations bounded by $O(\log d/\epsilon^2)$, which outperforms existing first-order methods.

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Hejian Sang, Jia Liu. 2018-05-23. Adaptive Stochastic Gradient Langevin Dynamics: Taming Convergence and Saddle Point Escape Time. https://arxiv.org/abs/1805.09416

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