# Stability of Finite-Batch Particle Mean-Field Variational Inference Beyond Strong Convexity

arXiv: https://arxiv.org/abs/2608.11486 · HTML: https://mlsanity.com/paper/2608.11486/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 39 references that are in the map.
- First posted on arXiv 11 Aug 2026.

## Builds on (most cited first, 22 of 22)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Non-asymptotic bounds for sampling algorithms without log-concavity](https://mlsanity.com/paper/1808.07105/) (2018)
- [The Tamed Unadjusted Langevin Algorithm](https://mlsanity.com/paper/1710.05559/) (2017)
- [Algorithms for mean-field variational inference via polyhedral optimization in the Wasserstein space](https://mlsanity.com/paper/2312.02849/) (2023)
- [Mean-field Variational Inference via Wasserstein Gradient Flow](https://mlsanity.com/paper/2207.08074/) (2022)
- [Regularized Stein Variational Gradient Flow](https://mlsanity.com/paper/2211.07861/) (2022)
- [On the Convergence of Coordinate Ascent Variational Inference](https://mlsanity.com/paper/2306.01122/) (2023)
- [Convergence of coordinate ascent variational inference for log-concave measures via optimal transport](https://mlsanity.com/paper/2404.08792/) (2024)
- [Error bounds for particle gradient descent, and extensions of the log-Sobolev and Talagrand inequalities](https://mlsanity.com/paper/2403.02004/) (2024)
- [Independent projections of diffusions: Gradient flows for variational inference and optimal mean field approximations](https://mlsanity.com/paper/2309.13332/) (2023)
- [Particle-based Variational Inference with Generalized Wasserstein Gradient Flow](https://mlsanity.com/paper/2310.16516/) (2023)
- [Convergence rate of random scan Coordinate Ascent Variational Inference under log-concavity](https://mlsanity.com/paper/2406.07292/) (2024)
- [Extending Mean-Field Variational Inference via Entropic Regularization: Theory and Computation](https://mlsanity.com/paper/2404.09113/) (2024)
- [Taming the Interacting Particle Langevin Algorithm: The Superlinear case](https://mlsanity.com/paper/2403.19587/) (2024)
- [A Particle Algorithm for Mean-Field Variational Inference](https://mlsanity.com/paper/2412.20385/) (2024)
- [Stability of Mean-Field Variational Inference](https://mlsanity.com/paper/2506.07856/) (2025)
- [Swarm-Based Gradient Descent Method for Non-Convex Optimization](https://mlsanity.com/paper/2211.17157/) (2022)
- [Swarm-based optimization with random descent](https://mlsanity.com/paper/2307.12441/) (2023)
- [Swarm-based gradient descent meets simulated annealing](https://mlsanity.com/paper/2404.18015/) (2024)
- [Variational inference via Gaussian interacting particles in the Bures-Wasserstein geometry](https://mlsanity.com/paper/2601.00632/) (2026)
- [Scalable Mean-Field Variational Inference via Preconditioned Primal-Dual Optimization](https://mlsanity.com/paper/2602.07632/) (2026)
- [Wasserstein Contraction of Coordinate Ascent Variational Inference](https://mlsanity.com/paper/2605.30253/) (2026)

## Abstract (arXiv)

We study the implementable finite-batch particle algorithm for mean-field variational inference as a fully discrete stochastic approximation of the projected Wasserstein dynamics. The target potential is globally smooth but need not be strongly convex. The departure from contractivity is quantified by the curvature defect [ mathfrak dα(x,y) = bigl[α|x-y|2- langlenabla V(x)-nabla V(y),x-yranglebigr]_+, ] which is the additive loss in the one-step Euler contraction estimate. We prove a non-asymptotic Wasserstein stability bound that separates initialization, product-empirical approximation, finite-batch drift error, time discretization, and the defects accumulated along the coupled trajectories. Under the uniform bound mathfrak dα≤β, the particle iterates remain within O(√β/α) of any MFVI minimizer, up to explicit errors in the particle number, batch size, and step size. The proof uses a stationary comparison array whose population law is an MFVI minimizer but whose particle-level law is a random product empirical measure, and it controls the resulting projected-drift discrepancy explicitly. We also give coordinatewise defect estimates and structural conditions for dimension-independent projected-drift sensitivity, construct an arbitrary-dimensional smooth nonconvex benchmark with a closed-form MFVI minimizer, and explain why polynomially growing drifts require a modification of the untamed explicit scheme.