Summary of the paper: This paper describes the use of a technique known as stochastic trust-region optimization in the context of variational inference (VI). In VI an objective needs to be maximized with respect to the parameters of an approximate distribution. This optimization task enforces that the approximate distribution q looks similar to the exact posterior. In complex probabilistic graphical models it is not possible to evaluate in closed form the objective. An alternative is to work with an stochastic estimate obtained by Monte Carlo.

We introduce TrustVI, a fast second-order algorithm for black-box variational inference based on trust-region optimization and the reparameterization trick. At each iteration, TrustVI proposes and assesses a step based on minibatches of draws from the variational distribution. We implemented TrustVI in the Stan framework and compared it to two alternatives: Automatic Differentiation Variational Inference (ADVI) and Hessian-free Stochastic Gradient Variational Inference (HFSGVI). The former is based on stochastic first-order optimization. The latter uses second-order information, but lacks convergence guarantees.