# Social Optima in Mean Field Linear-Quadratic-Gaussian Control with Volatility Uncertainty

arXiv: https://arxiv.org/abs/1912.06371 · HTML: https://mlsanity.com/paper/1912.06371/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Dec 2019.

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

- [Robust Q-learning for mean-field control under Wasserstein uncertainty in common noise](https://mlsanity.com/paper/2606.20356/) (2026)
- [Inverse reinforcement learning for indefinite mean-field social optimization with multiplicative noise](https://mlsanity.com/paper/2608.07252/) (2026)

## Abstract (arXiv)

This paper examines mean field linear-quadratic-Gaussian (LQG) social optimum control with volatility-uncertain common noise. The diffusion terms in the dynamics of agents contain an unknown volatility process driven by a common noise. We apply a robust optimization approach in which all agents view volatility uncertainty as an adversarial player. Based on the principle of person-by-person optimality and a two-step-duality technique for stochastic variational analysis, we construct an auxiliary optimal control problem for a representative agent. Through solving this problem combined with a consistent mean field approximation, we design a set of decentralized strategies, which are further shown to be asymptotically social optimal by perturbation analysis.