马尔可夫过程最优控制的回归-后期蒙特卡罗方法
Regress-Later Monte Carlo for optimal control of Markov processes
摘要：
我们发展了两种回归蒙特卡罗算法（数值迭代和性能迭代）来解决离散时间马尔可夫过程的最优随机控制的一般问题。我们制定我们的方法在一个创新的框架，使我们能够证明我们的数值方案的收敛速度。我们依赖于Regress Later方法，而不像其他尝试使用Regress Now技术。我们利用误差界，在我们的证明，以及数值实验，研究价值和性能迭代方法之间的差异。在Tsitsiklis和VanRoy [2001]和Longstaff和Schwartz [2001]中分别介绍了它们的特性，在文献中很大程度上没有注意到;然而，我们表明它们的差异在随机控制问题的实际解决方案中是至关重要的。最后，我们提供了一些准则，我们的算法的调整。
英文摘要：
We develop two Regression Monte Carlo algorithms (value and performance iteration) to solve general problems of optimal stochastic control of discrete-time Markov processes. We formulate our method within an innovative framework that allow us to prove the speed of convergence of our numerical schemes. We rely on the Regress Later approach unlike other attempts which employ the Regress Now technique. We exploit error bounds obtained in our proofs, along with numerical experiments, to investigate differences between the value and performance iteration approaches. Introduced in Tsitsiklis and VanRoy [2001] and Longstaff and Schwartz [2001] respectively, their characteristics have gone largely unnoticed in the literature; we show however that their differences are paramount in practical solution of stochastic control problems. Finally, we provide some guidelines for the tuning of our algorithms.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
