# A Fast Proximal Gradient Method and Convergence Analysis for Dynamic Mean Field Planning

arXiv: https://arxiv.org/abs/2102.13260 · HTML: https://mlsanity.com/paper/2102.13260/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Feb 2021.

## Built on by (most cited first, 4 of 4)

- [Bridging Mean-Field Games and Normalizing Flows with Trajectory Regularization](https://mlsanity.com/paper/2206.14990/) (2022)
- [A scalable deep learning approach for solving high-dimensional dynamic optimal transport](https://mlsanity.com/paper/2205.07521/) (2022)
- [Unsupervised Solution Operator Learning for Mean-Field Games via Sampling-Invariant Parametrizations](https://mlsanity.com/paper/2401.15482/) (2024)
- [Self-supervised In-context Operator Learning for Stochastic Mean-Field Control](https://mlsanity.com/paper/2608.18282/) (2026)

## Abstract (arXiv)

In this paper, we propose an efficient and flexible algorithm to solve dynamic mean-field planning problems based on an accelerated proximal gradient method. Besides an easy-to-implement gradient descent step in this algorithm, a crucial projection step becomes solving an elliptic equation whose solution can be obtained by conventional methods efficiently. By induction on iterations used in the algorithm, we theoretically show that the proposed discrete solution converges to the underlying continuous solution as the grid size increases. Furthermore, we generalize our algorithm to mean-field game problems and accelerate it using multilevel and multigrid strategies. We conduct comprehensive numerical experiments to confirm the convergence analysis of the proposed algorithm, to show its efficiency and mass preservation property by comparing it with state-of-the-art methods, and to illustrates its flexibility for handling various mean-field variational problems.