论文标题
通过本地职业措施的随机最佳控制
Stochastic Optimal Control via Local Occupation Measures
论文作者
论文摘要
事实证明，通过职业措施的视角查看随机过程是对随机最佳控制问题的理论和计算分析的强大攻击角度。我们提出了对传统职业测量框架的简单修改，该框架是通过在控制问题时空域的分区上在本地解决职业措施而得出的。该局部职业措施的这种概念为结构化半决赛编程的构建提供了精细的控制，以通过嵌入式扩散和跳跃过程通过力矩较量的层次结构进行丰富的随机最佳控制问题。因此，它弥合了基于离散化的近似值与汉密尔顿 - 雅各比 - 贝尔曼方程与占用度量弛豫之间的差距。我们用示例证明，这种方法可以计算高质量的界限，以相对于传统的职业衡量框架，大量随机的最佳控制问题的最佳价值具有显着的性能增长。
Viewing stochastic processes through the lens of occupation measures has proved to be a powerful angle of attack for the theoretical and computational analysis of stochastic optimal control problems. We present a simple modification of the traditional occupation measure framework derived from resolving the occupation measures locally on a partition of the control problem's space-time domain. This notion of local occupation measures provides fine-grained control over the construction of structured semidefinite programming relaxations for a rich class of stochastic optimal control problems with embedded diffusion and jump processes via the moment-sum-of-squares hierarchy. As such, it bridges the gap between discretization-based approximations to the Hamilton-Jacobi-Bellmann equations and occupation measure relaxations. We demonstrate with examples that this approach enables the computation of high quality bounds for the optimal value of a large class of stochastic optimal control problems with significant performance gains relative to the traditional occupation measure framework.
