2025年11月17日杂记 - Optimal Control

方法比较

• non linear Hamilton-Jacobi partial differential approach

  • 理论完备、可以找到全局最小值

  • 计算复杂度高, 维数灾难

• Lagrange principle

  • 计算复杂度低, 适合高维问题

  • 只能找到局部最优解, 通常伴随正则化方法会引入额外误差

  • (so far) has no efficient implementation in the natural stochastic setting with adapted Markov controls, while the Hamilton-Jacobi PDE approach directly extends to such stochastic controls; as a consequence computations of stochastic controls is basically limited to low dimensional problems.