论文标题
随机多阶段优化中参数凸价值函数的不同性和正则化
Differentiability and Regularization of Parametric Convex Value Functions in Stochastic Multistage Optimization
论文作者
论文摘要
在多阶段决策问题中，通常情况下，最初的战略决策（例如投资）之后是许多运营（运营投资）。这种最初的战略决策可以看作是影响多阶段决策问题的参数。更普遍地，我们在本文中研究了标准的多阶段随机优化问题，具体取决于参数。固定参数后，随机动态编程提供了一种计算问题最佳值的方法。因此，值函数既取决于状态（如往常）和参数。我们的目的是调查在存在这些对象时有效计算相对于参数的价值函数的梯度的可能性。当不相同的情况下，我们提出一种基于莫罗 - 耶西达包膜的正则化方法。我们提出了来自日前功率调度的数值测试案例。
In multistage decision problems, it is often the case that an initial strategic decision (such as investment) is followed by many operational ones (operating the investment). Such initial strategic decision can be seen as a parameter affecting a multistage decision problem. More generally, we study in this paper a standard multistage stochastic optimization problem depending on a parameter. When the parameter is fixed, Stochastic Dynamic Programming provides a way to compute the optimal value of the problem. Thus, the value function depends both on the state (as usual) and on the parameter. Our aim is to investigate on the possibility to efficiently compute gradients of the value function with respect to the parameter, when these objects exist. When nondifferentiable, we propose a regularization method based on the Moreau-Yosida envelope. We present a numerical test case from day-ahead power scheduling.
