论文标题
线性二次平均场社会优化：渐近可溶性和分散控制
Linear quadratic mean field social optimization: Asymptotic solvability and decentralized control
论文作者
论文摘要
本文研究了线性二次（LQ）平均野外社会优化问题的渐近可溶性，并具有受控扩散以及不确定的状态和控制权重。从$ n $ agent模型开始，我们采用了一种重新制定方法来得出低维的Riccati普通微分方程（ODE）系统，该系统表征了渐近溶解性的必要条件。从平均场限制获得的分散控制可确保最小化的最佳最佳损失，使社会成本具有幅度$ o（n）$，这意味着每个代理商的最佳损失$ O（1/n）$。我们进一步量化了相对于平均现场游戏解决方案的社会最佳效率提高。
This paper studies asymptotic solvability of a linear quadratic (LQ) mean field social optimization problem with controlled diffusions and indefinite state and control weights. Starting with an $N$-agent model, we employ a rescaling approach to derive a low-dimensional Riccati ordinary differential equation (ODE) system, which characterizes a necessary and sufficient condition for asymptotic solvability. The decentralized control obtained from the mean field limit ensures a bounded optimality loss in minimizing the social cost having magnitude $O(N)$, which implies an optimality loss of $O(1/N)$ per agent. We further quantify the efficiency gain of the social optimum with respect to the solution of the mean field game.
