  Achieving the full promise of the Thermodynamic Variational Objective (TVO),
a recently proposed variational lower bound on the log evidence involving a
one-dimensional Riemann integral approximation, requires choosing a "schedule"
of sorted discretization points. This paper introduces a bespoke Gaussian
process bandit optimization method for automatically choosing these points. Our
approach not only automates their one-time selection, but also dynamically
adapts their positions over the course of optimization, leading to improved
model learning and inference. We provide theoretical guarantees that our bandit
optimization converges to the regret-minimizing choice of integration points.
Empirical validation of our algorithm is provided in terms of improved learning
and inference in Variational Autoencoders and Sigmoid Belief Networks.
