# Stein Variational Gradient Descent Without Gradient

arXiv: https://arxiv.org/abs/1806.02775 · HTML: https://mlsanity.com/paper/1806.02775/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Jun 2018.

## Built on by (most cited first, 12 of 12)

- [Oops I Took A Gradient: Scalable Sampling for Discrete Distributions](https://mlsanity.com/paper/2102.04509/) (2021)
- [Annealed Stein Variational Gradient Descent](https://mlsanity.com/paper/2101.09815/) (2021)
- [Probabilistic Inference of Simulation Parameters via Parallel Differentiable Simulation](https://mlsanity.com/paper/2109.08815/) (2021)
- [Targeted Separation and Convergence with Kernel Discrepancies](https://mlsanity.com/paper/2209.12835/) (2022)
- [Batch Bayesian optimisation via density-ratio estimation with guarantees](https://mlsanity.com/paper/2209.10715/) (2022)
- [Coin Sampling: Gradient-Based Bayesian Inference without Learning Rates](https://mlsanity.com/paper/2301.11294/) (2023)
- [Guided Discrete Diffusion for Electronic Health Record Generation](https://mlsanity.com/paper/2404.12314/) (2024)
- [Stein Variational Gradient Descent with Multiple Kernel](https://mlsanity.com/paper/2107.09338/) (2021)
- [Stein Variational Evolution Strategies](https://mlsanity.com/paper/2410.10390/) (2024)
- [Low Stein Discrepancy via Message-Passing Monte Carlo](https://mlsanity.com/paper/2503.21103/) (2025)
- [Factor Representation and Decision Making in Stock Markets Using Deep Reinforcement Learning](https://mlsanity.com/paper/2108.01758/) (2021)
- [Variational Inference via Entropic Transport Descent](https://mlsanity.com/paper/2606.25265/) (2026)

## Abstract (arXiv)

Stein variational gradient decent (SVGD) has been shown to be a powerful approximate inference algorithm for complex distributions. However, the standard SVGD requires calculating the gradient of the target density and cannot be applied when the gradient is unavailable. In this work, we develop a gradient-free variant of SVGD (GF-SVGD), which replaces the true gradient with a surrogate gradient, and corrects the induced bias by re-weighting the gradients in a proper form. We show that our GF-SVGD can be viewed as the standard SVGD with a special choice of kernel, and hence directly inherits the theoretical properties of SVGD. We shed insights on the empirical choice of the surrogate gradient and propose an annealed GF-SVGD that leverages the idea of simulated annealing to improve the performance on high dimensional complex distributions. Empirical studies show that our method consistently outperforms a number of recent advanced gradient-free MCMC methods.