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  • title: Mirror Descent with Relative Smoothness in Measure Spaces, with application to Sinkhorn and Expectation-Maximization (EM)
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            Mirror Descent with Relative Smoothness in Measure Spaces, with application to Sinkhorn and Expectation-Maximization (EM)
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            Mirror Descent with Relative Smoothness in Measure Spaces, with application to Sinkhorn and Expectation-Maximization (EM)

            Nov 28, 2022

            Speakers

            PA

            Pierre-Cyril Aubin-Frankowski

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            Anna Korba

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            FL

            Flavien Léger

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            About

            Many problems in machine learning can be formulated as optimizing a convex functional over a space of measures. This paper studies the convergence of the mirror descent algorithm in this infinite-dimensional setting. Defining Bregman divergences through directional derivatives, we derive the convergence of the scheme for relatively smooth and strongly convex pairs of functionals. Applying our result to joint distributions and the Kullback-Leibler (KL) divergence, we show that Sinkhorn's primal i…

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