论文标题
离散时间线性季度平均场游戏的近似平衡计算
Approximate Equilibrium Computation for Discrete-Time Linear-Quadratic Mean-Field Games
论文作者
论文摘要
尽管平均场游戏（MFGS）的主题相对较长，但迄今为止，关于计算平衡控制策略的算法的工作有限。在本文中，我们开发了一种可计算的策略迭代算法，用于近似于折现成本的线性二次MFG中的平均场平衡。鉴于平均场，每个代理都面临线性二次跟踪问题，其解决方案涉及在逆行时间内演变的动态系统。这使得远期算法的开发更具挑战性。通过识别平均场更新运算符的结构属性，即它保留了特定形式的序列，我们开发了一种远程平衡计算算法。提供了量化计算的平均场平衡准确性作为算法停止条件的函数的界限。计算平衡的最优性是数值验证的。与最新的/并发结果相反，我们的算法似乎是第一个研究具有非平均平均场平衡的无限 - 摩尼斯MFG，尽管重点是线性二次设置。
While the topic of mean-field games (MFGs) has a relatively long history, heretofore there has been limited work concerning algorithms for the computation of equilibrium control policies. In this paper, we develop a computable policy iteration algorithm for approximating the mean-field equilibrium in linear-quadratic MFGs with discounted cost. Given the mean-field, each agent faces a linear-quadratic tracking problem, the solution of which involves a dynamical system evolving in retrograde time. This makes the development of forward-in-time algorithm updates challenging. By identifying a structural property of the mean-field update operator, namely that it preserves sequences of a particular form, we develop a forward-in-time equilibrium computation algorithm. Bounds that quantify the accuracy of the computed mean-field equilibrium as a function of the algorithm's stopping condition are provided. The optimality of the computed equilibrium is validated numerically. In contrast to the most recent/concurrent results, our algorithm appears to be the first to study infinite-horizon MFGs with non-stationary mean-field equilibria, though with focus on the linear quadratic setting.
