Non-convex Learning via Replica Exchange Stochastic Gradient MCMC

Wei Deng, Qi Feng, Liyao Gao, Faming Liang, Guang Lin
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:2474-2483, 2020.

Abstract

Replica exchange Monte Carlo (reMC), also known as parallel tempering, is an important technique for accelerating the convergence of the conventional Markov Chain Monte Carlo (MCMC) algorithms. However, such a method requires the evaluation of the energy function based on the full dataset and is not scalable to big data. The naïve implementation of reMC in mini-batch settings introduces large biases, which cannot be directly extended to the stochastic gradient MCMC (SGMCMC), the standard sampling method for simulating from deep neural networks (DNNs). In this paper, we propose an adaptive replica exchange SGMCMC (reSGMCMC) to automatically correct the bias and study the corresponding properties. The analysis implies an acceleration-accuracy trade-off in the numerical discretization of a Markov jump process in a stochastic environment. Empirically, we test the algorithm through extensive experiments on various setups and obtain the state-of-the-art results on CIFAR10, CIFAR100, and SVHN in both supervised learning and semi-supervised learning tasks.

Cite this Paper


BibTeX
@InProceedings{pmlr-v119-deng20b, title = {Non-convex Learning via Replica Exchange Stochastic Gradient {MCMC}}, author = {Deng, Wei and Feng, Qi and Gao, Liyao and Liang, Faming and Lin, Guang}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, pages = {2474--2483}, year = {2020}, editor = {Hal Daumé III and Aarti Singh}, volume = {119}, series = {Proceedings of Machine Learning Research}, month = {13--18 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v119/deng20b/deng20b.pdf}, url = { http://proceedings.mlr.press/v119/deng20b.html }, abstract = {Replica exchange Monte Carlo (reMC), also known as parallel tempering, is an important technique for accelerating the convergence of the conventional Markov Chain Monte Carlo (MCMC) algorithms. However, such a method requires the evaluation of the energy function based on the full dataset and is not scalable to big data. The naïve implementation of reMC in mini-batch settings introduces large biases, which cannot be directly extended to the stochastic gradient MCMC (SGMCMC), the standard sampling method for simulating from deep neural networks (DNNs). In this paper, we propose an adaptive replica exchange SGMCMC (reSGMCMC) to automatically correct the bias and study the corresponding properties. The analysis implies an acceleration-accuracy trade-off in the numerical discretization of a Markov jump process in a stochastic environment. Empirically, we test the algorithm through extensive experiments on various setups and obtain the state-of-the-art results on CIFAR10, CIFAR100, and SVHN in both supervised learning and semi-supervised learning tasks.} }
Endnote
%0 Conference Paper %T Non-convex Learning via Replica Exchange Stochastic Gradient MCMC %A Wei Deng %A Qi Feng %A Liyao Gao %A Faming Liang %A Guang Lin %B Proceedings of the 37th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2020 %E Hal Daumé III %E Aarti Singh %F pmlr-v119-deng20b %I PMLR %P 2474--2483 %U http://proceedings.mlr.press/v119/deng20b.html %V 119 %X Replica exchange Monte Carlo (reMC), also known as parallel tempering, is an important technique for accelerating the convergence of the conventional Markov Chain Monte Carlo (MCMC) algorithms. However, such a method requires the evaluation of the energy function based on the full dataset and is not scalable to big data. The naïve implementation of reMC in mini-batch settings introduces large biases, which cannot be directly extended to the stochastic gradient MCMC (SGMCMC), the standard sampling method for simulating from deep neural networks (DNNs). In this paper, we propose an adaptive replica exchange SGMCMC (reSGMCMC) to automatically correct the bias and study the corresponding properties. The analysis implies an acceleration-accuracy trade-off in the numerical discretization of a Markov jump process in a stochastic environment. Empirically, we test the algorithm through extensive experiments on various setups and obtain the state-of-the-art results on CIFAR10, CIFAR100, and SVHN in both supervised learning and semi-supervised learning tasks.
APA
Deng, W., Feng, Q., Gao, L., Liang, F. & Lin, G.. (2020). Non-convex Learning via Replica Exchange Stochastic Gradient MCMC. Proceedings of the 37th International Conference on Machine Learning, in Proceedings of Machine Learning Research 119:2474-2483 Available from http://proceedings.mlr.press/v119/deng20b.html .

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