Existence of optimal potentials for entropic optimal transport is a well studied particularly under assumptions of either finiteness in space or $L^\infty$ bounds on the cost function. We will discuss how these previous assumptions allowed for convergence in Total Variation of marginals to be sufficient for existence of maximisers. In fact the marginals converge in Kullback-Leibler Divergence, using the Fenchell-Young inequality this allows for the extension to the case of finite exponential moments.

Bio: Zachary Brannan is a PhD student studying at the university of Ottawa under the supervision of Dr Augusto Gerolin. He studies topic optimal transport with current interests in the theoretical grounding of Entorpic Optimal Transport and the design and use of Optimal transport based algorithms for DFT.