# Stochastic Particle-Optimization Sampling and the Non-Asymptotic Convergence Theory

arXiv: https://arxiv.org/abs/1809.01293 · HTML: https://mlsanity.com/paper/1809.01293/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Sep 2018.

## Built on by (most cited first, 20 of 20)

- [Towards Building the Federated GPT: Federated Instruction Tuning](https://mlsanity.com/paper/2305.05644/) (2023)
- [Particle Guidance: non-I.I.D. Diverse Sampling with Diffusion Models](https://mlsanity.com/paper/2310.13102/) (2023)
- [Fed-CBS: A Heterogeneity-Aware Client Sampling Mechanism for Federated Learning via Class-Imbalance Reduction](https://mlsanity.com/paper/2209.15245/) (2022)
- [Annealed Stein Variational Gradient Descent](https://mlsanity.com/paper/2101.09815/) (2021)
- [On Stein Variational Neural Network Ensembles](https://mlsanity.com/paper/2106.10760/) (2021)
- [SLED: Self Logits Evolution Decoding for Improving Factuality in Large Language Models](https://mlsanity.com/paper/2411.02433/) (2024)
- [Learning Equivariant Energy Based Models with Equivariant Stein Variational Gradient Descent](https://mlsanity.com/paper/2106.07832/) (2021)
- [Interacting Contour Stochastic Gradient Langevin Dynamics](https://mlsanity.com/paper/2202.09867/) (2022)
- [Feature Space Particle Inference for Neural Network Ensembles](https://mlsanity.com/paper/2206.00944/) (2022)
- [GAD-PVI: A General Accelerated Dynamic-Weight Particle-Based Variational Inference Framework](https://mlsanity.com/paper/2312.16429/) (2023)
- [DPVI: A Dynamic-Weight Particle-Based Variational Inference Framework](https://mlsanity.com/paper/2112.00945/) (2021)
- [Training Bayesian Neural Networks with Sparse Subspace Variational Inference](https://mlsanity.com/paper/2402.11025/) (2024)
- [Stein Variational Gradient Descent with Multiple Kernel](https://mlsanity.com/paper/2107.09338/) (2021)
- [Uncertainty for SVBRDF Acquisition using Frequency Analysis](https://mlsanity.com/paper/2406.17774/) (2024)
- [De-randomizing MCMC dynamics with the diffusion Stein operator](https://mlsanity.com/paper/2110.03768/) (2021)
- [ARTIST: Improving the Generation of Text-rich Images with Disentangled Diffusion Models and Large Language Models](https://mlsanity.com/paper/2406.12044/) (2024)
- [MLLM-LLaVA-FL: Multimodal Large Language Model Assisted Federated Learning](https://mlsanity.com/paper/2409.06067/) (2024)
- [Stein Variational Evolution Strategies](https://mlsanity.com/paper/2410.10390/) (2024)
- [Stein Diffusion Guidance: Training-Free Posterior Correction for Sampling Beyond High-Density Regions](https://mlsanity.com/paper/2507.05482/) (2025)
- [Multirate Stein Variational Gradient Descent for Efficient Bayesian Sampling](https://mlsanity.com/paper/2604.03981/) (2026)

## Abstract (arXiv)

Particle-optimization-based sampling (POS) is a recently developed effective sampling technique that interactively updates a set of particles. A representative algorithm is the Stein variational gradient descent (SVGD). We prove, under certain conditions, SVGD experiences a theoretical pitfall, it i.e., particles tend to collapse. As a remedy, we generalize POS to a stochastic setting by injecting random noise into particle updates, thus yielding particle-optimization sampling (SPOS). Notably, for the first time, we develop em non-asymptotic convergence theory for the SPOS framework (related to SVGD), characterizing algorithm convergence in terms of the 1-Wasserstein distance w.r.t.! the numbers of particles and iterations. Somewhat surprisingly, with the same number of updates (not too large) for each particle, our theory suggests adopting more particles does not necessarily lead to a better approximation of a target distribution, due to limited computational budget and numerical errors. This phenomenon is also observed in SVGD and verified via an experiment on synthetic data. Extensive experimental results verify our theory and demonstrate the effectiveness of our proposed framework.