Pathwise Stochastic Optimal Control
Pathwise Stochastic Optimal Control
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DOI：
10.1137/050642885
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发表时间：
2007-06
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影响因子：
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通讯作者：
L. Rogers
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文献类型：
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作者：
L. Rogers
本文研究离散时间受控马尔可夫过程的最优控制问题，通过将问题的值表示为对偶拉格朗日形式，该值表示为一族拉格朗日鞅上的下确界，该下确界的期望是目标的路径上确界被拉格朗日鞅项调整。这种表示形式为基于蒙特卡罗模拟的数值方法提供了可能，这在高维问题或复杂约束问题中可能是有利的。
This paper approaches optimal control problems for discrete-time controlled Markov processes by representing the value of the problem in a dual Lagrangian form; the value is expressed as an infimum over a family of Lagrangian martingales of an expectation of a pathwise supremum of the objective adjusted by the Lagrangian martingale term. This representation opens up the possibility of numerical methods based on Monte Carlo simulation, which may be advantageous in high-dimensional problems or in problems with complicated constraints.