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Explore entropic regularization techniques for optimal transport problems and their extensions to martingale transport in this 35-minute conference lecture. Learn how the entropic regularization of the classical quadratic optimal transport control problem, also known as the Schrödinger problem, can be extended to numerically solve drift controlled diffusion processes. Discover the time discretization approach for relative entropy that characterizes linear time scaling, preventing the relative entropy between diffusion processes from diverging when dealing with singular cases, leading to the concept of "Specific Relative Entropy." Examine how classical entropic optimal numerical methods, including the Sinkhorn algorithm, can be generalized to handle diffusion controlled diffusion processes, providing powerful computational tools for optimal martingale transport problems.
