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<span style="font-size: 12pt;"><b>"Methods of machine learning in stochastic control and high dimensional PDEs"</b></span>
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<div><b>Arash Fahim</b></div>
<div><b>Department of Mathematics,</b></div>
<div><b>Florida State University</b></div>
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<div><i>NOTE: Please feel free to forward/share this invitation with other groups/disciplines that might be interested in this talk/topic. All are welcome to attend.
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<div><b>https://fsu.zoom.us/j/94273595552 </b></div>
<div>Meeting # <b>942 7359 5552 </b></div>
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<div><b>Apr 6, 2022</b>, Schedule: </div>
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<div>* <b>3:00 to 3:30</b> PM Eastern Time (US and Canada) </div>
<div><b>Teatime</b> - Virtual (via Zoom)<br>
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<div>* <b>3:30 to 4:30</b> PM Eastern Time (US and Canada)<br>
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<div><b>Colloquium</b> - Attend F2F (in 499 DSL) or Virtually (via Zoom)<br>
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<div><b>Abstract: </b></div>
<div>In this talk, a review of numerical methods for stochastic control problems is presented, with emphasis on the most recent methods via machine learning. A major advantage of machine learning methods is tractability in high dimensions, e.g., d=100. An optimization
problems can simply be solved by a suitable version of gradient descent algorithm. A stochastic control problem requires an adaptability of the solution to the historical information. In order to address this, we write the dynamic programing principle for
the control problem through backward stochastic differential equation, which is equivalent to Hamilton-Jacobi-Bellman (HJB) PDE for the control problem. Then, we formulate loss function such that the solution to machine learning problem approximately solves
the dynamic programing equation. In addition, finding gradient and Hessian of the the solution of the HJB in high dimension is costly. We adopt a Monte Carlo method to remove dependence of the loss function to the gradient and Hessian as they are present in
the PDE.</div>
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