First, note that we shall use the same MDPs defined in Appendix D.1 as follows

In this paper, we are particularly interested in understanding whether, and how, the choice of distributional robustness bears statistical implications in learning the desired policy, by studying the sample complexity in the widely-used generative model (Kearns and Singh, 1999).

A Bayesian pseudocoreset is a compact synthetic dataset summarizing essential information of a large-scale dataset and thus can be used as a proxy dataset for scalable Bayesian inference. Typically, a Bayesian pseudocoreset is constructed by minimizing a divergence measure between the posterior conditioning on the pseudocoreset and the posterior conditioning on the full dataset. However, evaluating the divergence can be challenging, particularly for the models like deep neural networks having high-dimensional parameters.

We consider the problem of variational Bayesian inference in a latent variable model where a (possibly complex) observed stochastic process is governed by the solution of a latent stochastic differential equation (SDE).

This section illustrates that (7) holds.

Gaussian mixture models (GMMs) are fundamental to machine learning due to their flexibility as approximating densities. However, uncertainty quantification of GMMs remains a challenge as differential entropy lacks a closed form.