论文标题
深盖尔金方法用于平均场控制问题
Deep Galerkin Method for Mean Field Control Problem
论文作者
论文摘要
我们考虑一个最佳控制问题，其中弱相互作用的药物的平均福利引起了人们的关注。我们将平均场控制问题视为N-Agent Control问题的流体近似，并通过有限状态空间，连续时间和有限的Horizon进行了设置。平均场控制问题的价值函数被描述为单纯形中汉密尔顿 - 雅各比 - 贝尔曼方程的独特粘度解。我们应用DGM来估计分布的价值函数和演变。我们还证明了通过神经网络收敛到分析解决方案的数值解决方案。
We consider an optimal control problem where the average welfare of weakly interacting agents is of interest. We examine the mean-field control problem as the fluid approximation of the N-agent control problem with the setup of finite-state space, continuous-time, and finite-horizon. The value function of the mean-field control problem is characterized as the unique viscosity solution of a Hamilton-Jacobi-Bellman equation in the simplex. We apply the DGM to estimate the value function and the evolution of the distribution. We also prove the numerical solution approximated by a neural network converges to the analytical solution.
