Non-convex Learning via Replica Exchange Stochastic Gradient MCMC

Part of Proceedings of the International Conference on Machine Learning 1 pre-proceedings (ICML 2020)

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Wei Deng, Qi Feng, Liyao Gao, Faming Liang, Guang Lin


Replica exchange method (RE), 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 na\"ive implementation of RE in mini-batch settings introduces large biases, which cannot be directly extended to the stochastic gradient MCMC (SG-MCMC), the standard sampling method for simulating from deep neural networks (DNNs). In this paper, we propose an adaptive replica exchange SG-MCMC (reSG-MCMC) 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.