# Large Sample Mean-Field Stochastic Optimization

arXiv: https://arxiv.org/abs/1906.08894 · HTML: https://mlsanity.com/paper/1906.08894/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jun 2019.

## Built on by (most cited first, 2 of 2)

- [From Score Learning to Discretized Sampling: An End-to-End Generalization Analysis of Diffusion Models](https://mlsanity.com/paper/2607.23226/) (2026)
- [Convergence analysis of controlled particle systems arising in deep learning: from finite to infinite sample size](https://mlsanity.com/paper/2404.05185/) (2024)

## Abstract (arXiv)

We study a class of sampled stochastic optimization problems, where the underlying state process has diffusive dynamics of the mean-field type. We establish the existence of optimal relaxed controls when the sample set has finite size. The core of our paper is to prove, via Gamma-convergence, that the minimizer of the finite sample relaxed problem converges to that of the limiting optimization problem. We connect the limit of the sampled objective functional to the unique solution, in the trajectory sense, of a nonlinear Fokker-Planck-Kolmogorov (FPK) equation in a random environment. We highlight the connection between the minimizers of our optimization problems and the optimal training weights of a deep residual neural network.