Progress on designing closed loop optimal control has been hindered by the difficulties associated with the curse of dimensionalityIn 2016Jiequn Han and I developed the first deep learning-based algorithm for solving high dimensional control problems.This opened up a lot of new possibilities including solving high dimensional partial differential equationshigh dimensional game theory problems, and of course,high dimensional control problems.In factsolving high dimensiona problems is now among the most active area in scientific computing. However, it has not been an easy task to turn these kinds of algorithms to practical use. I will review the progress made so far as well as the difficulties in this area. I will discuss applications to the control ofrobotic arms, as well as to macro-economics. The work presented is joint work with a lot ofpeopleparticularly Jiequn Han Wei Hu,Jihao Long,Yucheng Yang,Xuanxi Zhang,Yue Zhao,Zhenghua Zhao

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