Stochastic gradient MCMC (SG-MCMC) has played an important role in large-scale Bayesian learning, with well-developed theoretical convergence properties. In such applications of SG-MCMC, it is becoming increasingly popular to employ distributed systems, where stochastic gradients are computed based on some outdated parameters, yielding what are termed stale gradients. While stale gradients could be directly used in SG-MCMC, their impact on convergence properties has not been well studied. In this paper we develop theory to show that while the bias and MSE of an SG-MCMC algorithm depend on the staleness of stochastic gradients, its estimation variance (relative to the expected estimate, based on a prescribed number of samples) is independent of it. In a simple Bayesian distributed system with SG-MCMC, where stale gradients are computed asynchronously by a set of workers, our theory indicates a linear speedup on the decrease of estimation variance w.r.t. the number of workers. Experiments on synthetic data and deep neural networks validate our theory, demonstrating the effectiveness and scalability of SG-MCMC with stale gradients.

在SG-MCMC中使用过期参数进行随机梯度计算在收敛性方面影响未知，但我们的理论表明，这仅影响偏差和均方误差，而估计方差与流逝度无关，在分布式系统中有一定的可扩展性和线性加速减少方差。

带有陈旧梯度的随机梯度MCMC