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Black-box variational inference (BBVI) now sees widespread use in machinelearning and statistics as a fast yet flexible alternative to Markov chainMonte Carlo methods for approximate Bayesian inference. However, stochasticoptimization methods for BBVI remain unreliable and require substantialexpertise and hand-tuning to apply effectively. In this paper, we proposeRobust, Automated, and Accurate BBVI (RAABBVI), a framework for reliable BBVIoptimization. RAABBVI is based on rigorously justified automation techniques,includes just a small number of intuitive tuning parameters, and detectsinaccurate estimates of the optimal variational approximation. RAABBVIadaptively decreases the learning rate by detecting convergence of thefixed--learning-rate iterates, then estimates the symmetrized Kullback--Leiber(KL) divergence between the current variational approximation and the optimalone. It also employs a novel optimization termination criterion that enablesthe user to balance desired accuracy against computational cost by comparing(i) the predicted relative decrease in the symmetrized KL divergence if asmaller learning were used and (ii) the predicted computation required toconverge with the smaller learning rate. We validate the robustness andaccuracy of RAABBVI through carefully designed simulation studies and on adiverse set of real-world model and data examples.

Robust, Automated, and Accurate Black-box Variational Inference