  Current objective functions used for training neural MCMC proposal
distributions implicitly rely on architectural restrictions to yield sensible
optimization results, which hampers the development of highly expressive neural
MCMC proposal architectures. In this work, we introduce and demonstrate a
semi-empirical procedure for determining approximate objective functions
suitable for optimizing arbitrarily parameterized proposal distributions in
MCMC methods. Our proposed Ab Initio objective functions consist of the
weighted combination of functions following constraints on their global optima
and transformation invariances that we argue should be upheld by general
measures of MCMC efficiency for use in proposal optimization. Our experimental
results demonstrate that Ab Initio objective functions maintain favorable
performance and preferable optimization behavior compared to existing objective
functions for neural MCMC optimization. We find that Ab Initio objective
functions are sufficiently robust to enable the confident optimization of
neural proposal distributions parameterized by deep generative networks
extending beyond the regimes of traditional MCMC schemes
