Computable primal and dual bounds for stochastic control
Computable primal and dual bounds for stochastic control
复制标题
随机控制的可计算原始边界和对偶边界
DOI：
10.1137/18m1232231
复制
发表时间：
2020
影响因子：
2.2
通讯作者：
Kawai Reiichiro
中科院分区：
文献类型：
--
作者：
Jiao Chunxi;Kawai Reiichiro
我们调查的线性规划框架的出口时间随机控制问题，并应用矩平方和的层次得到紧逐点界和全局边界函数的价值函数。适当的措施和对偶线性规划的测试功能的原始线性规划的数值实现的半定规划的目标时刻和平方和多项式表示，分别。在适当的技术条件下，当多项式次数增加到无穷大时，数值优化的边界从下面收敛到值函数。我们专注于对偶问题，这是特别有效的，因为它的单一实现产生一个多项式边界函数在整个问题域，因为它允许灵活的选择目标函数，可以提高全球范围内的利益。
We investigate the linear programming framework for an exit-time stochastic control problem and apply the moment-sum-of-squares hierarchy to obtain tight pointwise bounds and global bounding functions for the value function. The primal linear program over suitable measures and the dual linear program over test functions are implemented numerically by semidefinite programs which target at moments and sum-of-squares polynomial representations, respectively. Numerically optimized bounds converge to the value function from below as polynomial degree increases to infinity under suitable technical conditions. We focus on the dual problem, which is particularly effective, as its single implementation yields a polynomial bounding function over the entire problem domain, and since it allows a flexible choice of objective function, one may improve the global bound on regions of interest.