Stochastic optimal control has been an effective tool for many decision problems. Although, they provide the much needed quantitative modeling for such problems, until recently they have been numerically intractable in high-dimensional settings. However, several recent studies that use deep neural networks report impressive numerical results in high dimensions when the structure of the uncertainty is assumed to be known. The main tool is a Monte-Carlo type algorithm combined with deep neural networks proposed by Han, E and Jentzen. In this talk, I will outline this approach and discuss its properties; in particular, the difficulties that data-driven problems face as opposed to model-driven ones. Numerical results, while validating the power of the method in high dimensions, they also show the dependence on the dimension and the size of the training data. This is joint work with Max Reppen of Boston University.

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https://umich.zoom.us/j/98619190605

Meeting ID: 986 1919 0605
Passcode: 286704

To request access to the Zoom video, please send an email to: math-mcaim@umich.edu
Speaker(s): Mete Soner (Princeton University, Department of Operations Research and Financial Engineering)