On sample size control in sample average approximations for solving smooth stochastic programs
On sample size control in sample average approximations for solving smooth stochastic programs
复制标题
求解平滑随机规划的样本平均近似中的样本大小控制
DOI：
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复制
发表时间：
2013
影响因子：
2.2
通讯作者：
J. Royset
中科院分区：
文献类型：
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作者：
J. Royset
我们考虑光滑随机规划和发展的离散时间最优控制问题，自适应选择样本大小的一类算法的基础上可变样本平均近似（VSAA）。控制问题的目标是最大限度地减少预期的计算成本，以获得一个随机规划的近最优解，并近似使用动态规划求解。最优控制问题取决于未知参数，如收敛速度、每次迭代的计算成本和采样误差。因此，我们在一个滚动时域框架内实现的方法，其中参数估计和最优控制问题的VSAA算法的计算过程中反复解决。由此产生的样本量选择政策始终产生近最优的解决方案，在短的计算时间相比，其他合理的政策，在几个数值例子。
We consider smooth stochastic programs and develop a discrete-time optimal-control problem for adaptively selecting sample sizes in a class of algorithms based on variable sample average approximations (VSAA). The control problem aims to minimize the expected computational cost to obtain a near-optimal solution of a stochastic program and is solved approximately using dynamic programming. The optimal-control problem depends on unknown parameters such as rate of convergence, computational cost per iteration, and sampling error. Hence, we implement the approach within a receding-horizon framework where parameters are estimated and the optimal-control problem is solved repeatedly during the calculations of a VSAA algorithm. The resulting sample-size selection policy consistently produces near-optimal solutions in short computing times as compared to other plausible policies in several numerical examples.