Large-Scale Empirical Study Compares 56 Optimization Algorithms for Black-Box Variational Inference
Researchers conducted a large-scale empirical evaluation of 56 stochastic optimization algorithms across 1,092 Bayesian inference problems, totaling over 550,000 optimization runs and 15 core-years of compute. The study addresses a core limitation of black-box variational inference (BBVI): that its underlying optimizers typically require extensive, problem-specific manual tuning. The findings establish a practical baseline for tuning-free inference, showing that running a portfolio of just 5 algorithms reliably approaches the best achievable performance.
Black-box variational inference is a widely used approach for approximating Bayesian posteriors via stochastic optimization, but its practical utility has been hampered by the need for problem-specific hyperparameter tuning. To address this, researchers from the machine learning and statistics community benchmarked 56 gradient-based optimization algorithms — spanning a broad range of modern adaptive methods — against 1,092 inference problems of varying difficulty. The benchmark problems covered posterior target dimensions from 1 to 10,000, condition numbers from 1 to 100 million, and multiple variational families, making it one of the most comprehensive evaluations of its kind. The study found that no single optimizer universally dominates across all problem types, a result that underscores the heterogeneity of real-world inference challenges. However, a key practical finding is that selecting a portfolio of 5 algorithms is sufficient to reliably achieve near-optimal performance without expert tuning. This provides both a strong empirical baseline for practitioners who cannot afford manual tuning and a rigorous reference point for researchers developing new stochastic optimization methods. The work was submitted to arXiv in June 2026 and has not yet undergone formal peer review.
What's missing
The paper has not yet undergone formal peer review, so its methodology and conclusions have not been independently validated. It is also unclear whether the benchmark problems are representative of real-world Bayesian modeling tasks outside the tested distributions.
What different sources said
- arXiv cs.LGCenter
Large-scale empirical tuning and comparison of default optimizers for variational inference
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