Fast and Correct Gradient-Based Optimisation for Probabilistic Programming via Smoothing

Abstract We study the foundations of variational inference, which frames posterior inference as an optimisation problem, for probabilistic programming. The dominant approach in practice is stochastic gradient descent. In particular, a variant using so-called reparameterisation estimator exhibits fast convergence traditional statistics setting. Unfortunately, discontinuities, are readily expressible programming languages, can compromise correctness this approach. consider simple (higher-order, probabilistic) language with conditionals, and we endow our both measurable smoothed (approximate) value semantics. present type systems establish technical pre-conditions. Thus prove descent to be correct when applied problem. Besides, solve original problem up any error tolerance by choosing accuracy coefficient suitably. Empirically demonstrate that has similar key competitor, but simpler, faster, attains orders magnitude reduction work-normalised variance.