SIAM Journal on Control and Optimization, Volume 59, Issue 2, Page 825-856, January 2021.
This paper examines mean field linear-quadratic-Gaussian 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.

中文翻译：

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具有波动率不确定性的均值线性二次高斯控制中的社会最优

SIAM控制与优化杂志，第59卷，第2期，第825-856页，2021年1月。
本文研究了具有波动性不确定公共噪声的均值线性二次高斯社会最优控制。代理动力学中的扩散项包含由共同噪声驱动的未知的波动过程。我们采用了一种鲁棒的优化方法，其中所有代理商都将波动性不确定性视为对手。基于人对人的最优性原理和随机变分分析的两步对偶技术，我们构造了代表智能体的辅助最优控制问题。通过解决此问题并结合一致的均值场逼近，我们设计了一套分散策略，通过摄动分析进一步证明了它们是渐近社会最优的。