Gaussian Process Bandit Optimization of the Thermodynamic Variational Objective
This work addresses a specific bottleneck in variational inference for machine learning practitioners, offering an incremental improvement over existing TVO methods.
The paper tackles the problem of selecting optimal discretization points for the Thermodynamic Variational Objective (TVO) by introducing a Gaussian process bandit optimization method that automates and dynamically adapts these points, leading to improved model learning and inference in Variational Autoencoders and Sigmoid Belief Networks.
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.