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We introduce TrustVI, a fast second-order algorithm for black-box variationalinference based on trust-region optimization and the reparameterization trick.At each iteration, TrustVI proposes and assesses a step based on minibatches ofdraws from the variational distribution. The algorithm provably converges to astationary point. We implemented TrustVI in the Stan framework and compared itto two alternatives: Automatic Differentiation Variational Inference (ADVI) andHessian-free Stochastic Gradient Variational Inference (HFSGVI). The former isbased on stochastic first-order optimization. The latter uses second-orderinformation, but lacks convergence guarantees. TrustVI typically converged atleast one order of magnitude faster than ADVI, demonstrating the value ofstochastic second-order information. TrustVI often found substantially bettervariational distributions than HFSGVI, demonstrating that our convergencetheory can matter in practice.

Fast Black-box Variational Inference through Stochastic Trust-Region Optimization