  Minimizing the inclusive Kullback-Leibler (KL) divergence with stochastic
gradient descent (SGD) is challenging since its gradient is defined as an
integral over the posterior. Recently, multiple methods have been proposed to
run SGD with biased gradient estimates obtained from a Markov chain. This paper
provides the first non-asymptotic convergence analysis of these methods by
establishing their mixing rate and gradient variance. To do this, we
demonstrate that these methods-which we collectively refer to as Markov chain
score ascent (MCSA) methods-can be cast as special cases of the Markov chain
gradient descent framework. Furthermore, by leveraging this new understanding,
we develop a novel MCSA scheme, parallel MCSA (pMCSA), that achieves a tighter
bound on the gradient variance. We demonstrate that this improved theoretical
result translates to superior empirical performance.

Machine Learning;Artificial Intelligence;Machine Learning