论文标题
随机编程的样本平均近似值具有相等性约束
Sample Average Approximation for Stochastic Programming with Equality Constraints
论文作者
论文摘要
我们重新审查非凸随机编程的样本平均近似方法（SAA）方法。我们表明，将SAA方法应用于具有期望值平等约束的问题并不一定会导致随着样本量增加而产生渐近最佳性保证。为了解决这个问题，我们放松平等约束。然后，我们证明在轻度平滑度和相等性约束函数上，修改后的SAA方法的渐近最优性。我们的分析使用随机集理论和浓度不平等来表征采样过程中的近似误差。我们将方法和分析应用于由Wiener过程建模的外部干扰下的非线性动力学系统的随机最佳控制问题。相关随机程序的数值结果显示了所提出的方法的可靠性。火箭驱动的下降问题的结果表明，与确定性基线相比，我们的计算解决方案允许显着降低不确定性。
We revisit the sample average approximation (SAA) approach for non-convex stochastic programming. We show that applying the SAA approach to problems with expected value equality constraints does not necessarily result in asymptotic optimality guarantees as the sample size increases. To address this issue, we relax the equality constraints. Then, we prove the asymptotic optimality of the modified SAA approach under mild smoothness and boundedness conditions on the equality constraint functions. Our analysis uses random set theory and concentration inequalities to characterize the approximation error from the sampling procedure. We apply our approach and analysis to the problem of stochastic optimal control for nonlinear dynamical systems under external disturbances modeled by a Wiener process. Numerical results on relevant stochastic programs show the reliability of the proposed approach. Results on a rocket-powered descent problem show that our computed solutions allow for significant uncertainty reduction compared to a deterministic baseline.
