Though with progress, model learning and performing posterior inference still
remains a common challenge for using deep generative models, especially for
handling discrete hidden variables. This paper is mainly concerned with
algorithms for learning Helmholz machines, which is characterized by pairing
the generative model with an auxiliary inference model. A common drawback of
previous learning algorithms is that they indirectly optimize some bounds of
the targeted marginal log-likelihood. In contrast, we successfully develop a
new class of algorithms, based on stochastic approximation (SA) theory of the
Robbins-Monro type, to directly optimize the marginal log-likelihood and
simultaneously minimize the inclusive KL-divergence. The resulting learning
algorithm is thus called joint SA (JSA). Moreover, we construct an effective
MCMC operator for JSA. Our results on the MNIST datasets demonstrate that the
JSA's performance is consistently superior to that of competing algorithms like
RWS, for learning a range of difficult models.

本文描述了一种新型基于随机逼近理论 (Robbins-Monro type) 的算法，直接优化边缘对数似然并同时最小化 KL 散度，以便更好地学习和应用针对离散隐藏变量的深度生成模型，称为联合随机逼近算法 (JSA)，并构建了一个有效的 MCMC 操作符用于优化 JSA 的表现。同时，在 MNIST 数据集上的实验表明，JSA 相对于类似 RWS 等算法，可以显著提高学习不同复杂度模型的性能。