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Automatic differentiation variational inference (ADVI) offers fast andeasy-to-use posterior approximation in multiple modern probabilisticprogramming languages. However, its stochastic optimizer lacks clearconvergence criteria and requires tuning parameters. Moreover, ADVI inheritsthe poor posterior uncertainty estimates of mean-field variational Bayes(MFVB). We introduce "deterministic ADVI" (DADVI) to address these issues.DADVI replaces the intractable MFVB objective with a fixed Monte Carloapproximation, a technique known in the stochastic optimization literature asthe "sample average approximation" (SAA). By optimizing an approximate butdeterministic objective, DADVI can use off-the-shelf second-order optimization,and, unlike standard mean-field ADVI, is amenable to more accurate posteriorcovariances via linear response (LR). In contrast to existing worst-casetheory, we show that, on certain classes of common statistical problems, DADVIand the SAA can perform well with relatively few samples even in very highdimensions, though we also show that such favorable results cannot extend tovariational approximations that are too expressive relative to mean-field ADVI.We show on a variety of real-world problems that DADVI reliably finds goodsolutions with default settings (unlike ADVI) and, together with LRcovariances, is typically faster and more accurate than standard ADVI.

Black Box Variational Inference with a Deterministic Objective: Faster, More Accurate, and Even More Black Box