# Mean-Field Generalisation Bounds for Learning Controls in Stochastic Environments

arXiv: https://arxiv.org/abs/2508.16001 · HTML: https://mlsanity.com/paper/2508.16001/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 44 references that are in the map.
- First posted on arXiv 21 Aug 2025.

## Builds on (most cited first, 21 of 21)

- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [Deep Double Descent: Where Bigger Models and More Data Hurt](https://mlsanity.com/paper/1912.02292/) (2019)
- [A Mean Field View of the Landscape of Two-Layers Neural Networks](https://mlsanity.com/paper/1804.06561/) (2018)
- [Deep Hedging](https://mlsanity.com/paper/1802.03042/) (2018)
- [Deep Learning Approximation for Stochastic Control Problems](https://mlsanity.com/paper/1611.07422/) (2016)
- [Mean-Field Langevin Dynamics and Energy Landscape of Neural Networks](https://mlsanity.com/paper/1905.07769/) (2019)
- [Towards a Complete Analysis of Langevin Monte Carlo: Beyond Poincar'e Inequality](https://mlsanity.com/paper/2303.03589/) (2023)
- [Deep neural networks algorithms for stochastic control problems on finite horizon: convergence analysis](https://mlsanity.com/paper/1812.04300/) (2018)
- [Recent Developments in Machine Learning Methods for Stochastic Control and Games](https://mlsanity.com/paper/2303.10257/) (2023)
- [Particle Dual Averaging: Optimization of Mean Field Neural Networks with Global Convergence Rate Analysis](https://mlsanity.com/paper/2012.15477/) (2020)
- [Convergence of Policy Gradient for Entropy Regularized MDPs with Neural Network Approximation in the Mean-Field Regime](https://mlsanity.com/paper/2201.07296/) (2022)
- [Quantitative Propagation of Chaos for SGD in Wide Neural Networks](https://mlsanity.com/paper/2007.06352/) (2020)
- [Deep neural networks algorithms for stochastic control problems on finite horizon: numerical applications](https://mlsanity.com/paper/1812.05916/) (2018)
- [Regularity and stability of feedback relaxed controls](https://mlsanity.com/paper/2001.03148/) (2020)
- [Deep Empirical Risk Minimization in finance: looking into the future](https://mlsanity.com/paper/2011.09349/) (2020)
- [Mean-field Analysis of Generalization Errors](https://mlsanity.com/paper/2306.11623/) (2023)
- [Efficient Learning for Entropy-Regularized Markov Decision Processes via Multilevel Monte Carlo](https://mlsanity.com/paper/2503.21224/) (2025)
- [Me, myself and I: a general theory of non-Markovian time-inconsistent stochastic control for sophisticated agents](https://mlsanity.com/paper/2002.12572/) (2020)
- [Non-convex entropic mean-field optimization via Best Response flow](https://mlsanity.com/paper/2505.22760/) (2025)
- [Limit Order Book Simulation and Trade Evaluation with K-Nearest-Neighbor Resampling](https://mlsanity.com/paper/2409.06514/) (2024)

## Abstract (arXiv)

We consider a data-driven formulation of the classical discrete-time stochastic control problem. Our approach exploits the natural structure of many such problems, in which significant portions of the system are uncontrolled. Employing the dynamic programming principle and the mean-field interpretation of single-hidden layer neural networks, we formulate the control problem as a series of infinite-dimensional minimisation problems. When regularised carefully, we provide practically verifiable assumptions for non-asymptotic bounds on the generalisation error achieved by the minimisers to this problem, thus ensuring stability in overparametrised settings, for controls learned using finitely many observations. We explore connections to the traditional noisy stochastic gradient descent algorithm, and subsequently show promising numerical results for some classic control problems.