SIAM Journal on Optimization, Volume 30, Issue 1, Page 407-438, January 2020.
We introduce an extension of stochastic dual dynamic programming (SDDP) to solve stochastic convex dynamic programming equations. This extension applies when some or all primal and dual subproblems to be solved along the forward and backward passes of the method are solved with bounded errors (inexactly). This inexact variant of SDDP is described for both linear problems (the corresponding variant being denoted by ISDDP-LP) and nonlinear problems (the corresponding variant being denoted by ISDDP-NLP). We prove convergence theorems for ISDDP-LP and ISDDP-NLP for both bounded and asymptotically vanishing errors. Finally, we present the results of numerical experiments comparing SDDP and ISDDP-LP on a portfolio problem with direct transaction costs modeled as a multistage stochastic linear optimization problem. In these experiments, ISDDP-LP allows us to strike a different balance between policy quality and computing time, trading off the former for the latter.

中文翻译：

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随机双重动态规划中的不精确削减

SIAM优化杂志，第30卷，第1期，第407-438页，2020年1月。
我们引入了随机双重动态规划（SDDP）的扩展来求解随机凸动态规划方程。当使用有限误差（不精确地）解决沿着方法的前向和后向传递要解决的一些或所有基本和对偶子问题时，将应用此扩展。针对线性问题（相应的变量由ISDDP-LP表示）和非线性问题（相应的变量由ISDDP-NLP表示）描述了SDDP的这种不精确的变体。我们证明了有界和渐近消失误差的ISDDP-LP和ISDDP-NLP的收敛定理。最后，我们提出了将SDDP和ISDDP-LP在直接交易成本建模为多阶段随机线性优化问题的投资组合问题上进行比较的数值实验结果。在这些实验中