Reproduce “Mirror Descent with Relative Smoothness in Measure Spaces, with application to Sinkhorn and EM” on OpenResearch
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About this paper
Pierre-Cyril Aubin-Frankowski, Anna Korba, Flavien Léger
The authors develop an entropy-aware mirror-descent framework for optimization over measures, where ordinary smoothness can fail. Using directional derivatives and relative smoothness, they establish sublinear objective-gap convergence, with a geometric rate under relative strong convexity. For continuous entropic optimal transport with bounded costs, primal Sinkhorn iterates satisfy an O(1/n) KL bound; the linear rate requires curvature on a restricted set.
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