mlsanityData to 7 Oct 2026

Linear Convergence of Black-Box Variational Inference: Should We Stick the Landing?

arXiv 2307.14642 ↗First posted 27 Jul 2023stat.ML cs.LG stat.COcited by 10

Not on the map. Why?

Abstract (arXiv)

We prove that black-box variational inference (BBVI) with control variates, particularly the sticking-the-landing (STL) estimator, converges at a geometric (traditionally called "linear") rate under perfect variational family specification. In particular, we prove a quadratic bound on the gradient variance of the STL estimator, one which encompasses misspecified variational families. Combined with previous works on the quadratic variance condition, this directly implies convergence of BBVI with the use of projected stochastic gradient descent. For the projection operator, we consider a domain with triangular scale matrices, which the projection onto is computable in Theta(d) time, where d is the dimensionality of the target posterior. We also improve existing analysis on the regular closed-form entropy gradient estimators, which enables comparison against the STL estimator, providing explicit non-asymptotic complexity guarantees for both.

Key facts. Cited by 10 papers in the map (data through 7 Oct 2026). Builds on 42 of its 82 references that are in the map. First posted on arXiv 27 Jul 2023.

Builds on

42 of 82 references.

References · 42

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30 more
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Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 4; 2025: 3; 2026: 3.

10 papers.

  1. 2024Kernel Semi-Implicit Variational Inferencecited by 8
  2. 2024On Divergence Measures for Training GFlowNetscited by 6
  3. 2024Efficient Mixture Learning in Black-Box Variational Inferencecited by 3
  4. 2025Natural Gradient VI: Guarantees for Non-Conjugate Modelscited by 3
  5. 2024Understanding and mitigating difficulties in posterior predictive evaluationcited by 1
  6. 2025AutoSGD: Automatic Learning Rate Selection for Stochastic Gradient Descentcited by 1
  7. 2025Nearly Dimension-Independent Convergence of Mean-Field Black-Box Variational Inferencecited by 1
  8. 2026A Kernel Approach for Semi-implicit Variational Inferencecited by 1
  9. 2026Stochastic Gradient Variational Inference with Price's Gradient Estimator from Bures-Wasserstein to Parameter Spacecited by 0
  10. 2026Large-scale empirical tuning and comparison of default optimizers for variational inferencecited by 0