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首页> 外文期刊>SIAM Journal on Optimization: A Publication of the Society for Industrial and Applied Mathematics >EXACT CONVERGING BOUNDS FOR STOCHASTIC DUAL DYNAMIC PROGRAMMING VIA FENCHEL DUALITY
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EXACT CONVERGING BOUNDS FOR STOCHASTIC DUAL DYNAMIC PROGRAMMING VIA FENCHEL DUALITY

机译：通过Fenchel Tuality的随机双动编程精确融合界限

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The stochastic dual dynamic programming (SDDP) algorithm has become one of the main tools used to address convex multistage stochastic optimal control problems. Recently a large amount of work has been devoted to improving the convergence speed of the algorithm through cut selection and regularization, and to extending the field of applications to nonlinear, integer, or risk-averse problems. However, one of the main downsides of the algorithm remains the difficulty in giving an upper bound of the optimal value, usually estimated through Monte Carlo methods and therefore difficult to use in the stopping criterion of the algorithm. In this paper we present a dual SDDP algorithm that yields a converging exact upper bound for the optimal value of the optimization problem. As an easy consequence of our approach, we show how to compute an alternative control policy based on an inner approximation of Bellman value functions instead of the outer approximation given by the standard SDDP algorithm. We illustrate the approach on an energy production problem involving zones of production and transportation links between the zones. The numerical experiments we carry out on this example show the effectiveness of the method.
机译：随机双动态编程（SDDP）算法已成为用于解决凸多级随机最佳控制问题的主要工具之一。最近，已经致力于通过切割选择和正规来提高算法的收敛速度，并将应用领域扩展到非线性，整数或风险厌恶问题。然而，该算法的主要缺陷之一仍然难以给出最佳值的上限，通常通过蒙特卡罗方法估计，因此难以在算法的停止标准中使用。在本文中，我们介绍了一种双SDDP算法，它产生了优化问题的最佳值的会聚精确界限。作为我们的方法的简单后果，我们展示了如何基于Bellman值函数的内部近似来计算替代控制策略，而不是由标准SDDP算法给出的外近似。我们说明了涉及区域之间的生产区和交通连接区的能源生产问题的方法。我们对该示例进行的数值实验显示了该方法的有效性。

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