论文标题
方案分解解决方案框架，用于不可分割的随机控制问题
Scenario-decomposition Solution Framework for Nonseparable Stochastic Control Problems
论文作者
论文摘要
当随机控制问题没有可分离性和/或单调性时，贝尔曼（Bellman）在1950年代开创的动态编程无法用作时间分解解决方案方法。多年来，此类案件在理论基础和解决方案方法中都对控制社会构成了巨大挑战。借助Rockafellar和Wets在1991年提出的进行性对冲算法的帮助，我们为随机控制问题开发了一种新的场景分解解决方案框架，该框架可能是不可分离的和/或非单调的，从而扩大了随机最佳控制的范围。然后，我们讨论其一些有希望的应用程序，包括在线二次编程问题和平滑属性的动态投资组合选择问题。
When stochastic control problems do not possess separability and/or monotonicity, the dynamic programming pioneered by Bellman in 1950s fails to work as a time-decomposition solution method. Such cases have posted a great challenge to the control society in both theoretical foundation and solution methodologies for many years. With the help of the progressive hedging algorithm proposed by Rockafellar and Wets in 1991, we develop a novel scenario-decomposition solution framework for stochastic control problems which could be nonseparable and/or non-monotonic, thus extending the reach of stochastic optimal control. We discuss then some of its promising applications, including online quadratic programming problems and dynamic portfolio selection problems with smoothing properties.
