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New math paper details optimization on Wasserstein space

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Researchers have developed new methods for optimizing functionals on Wasserstein spaces, a mathematical concept crucial for understanding probability distributions. The work establishes linear convergence for proximal descent schemes, relaxing previous requirements for geodesic convexity. This advancement utilizes a uniform logarithmic Sobolev inequality and an entropy "sandwich" lemma, extending prior research and addressing challenges related to the definition of relative Fisher information within the scheme. AI

RANK_REASON The cluster contains a single academic paper published on arXiv. [lever_c_demoted from research: ic=1 ai=0.4]

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New math paper details optimization on Wasserstein space

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  1. arXiv cs.LG TIER_1 English(EN) · Razvan-Andrei Lascu, Mateusz B. Majka, David \v{S}i\v{s}ka, {\L}ukasz Szpruch ·

    Linear convergence of proximal descent schemes on the Wasserstein space

    arXiv:2411.15067v2 Announce Type: replace-cross Abstract: We investigate proximal descent methods, inspired by the minimizing movement scheme introduced by Jordan, Kinderlehrer and Otto, for optimizing entropy-regularized functionals on the Wasserstein space. We establish linear …

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