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Free, publicly-accessible full text available September 4, 2026
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Algorithms for mean-field variational inference via polyhedral optimization in the Wasserstein spaceWe develop a theory of finite-dimensional polyhedral subsets over the Wasserstein space and optimization of functionals over them via first-order methods. Our main application is to the problem of mean-field variational inference, which seeks to approximate a distribution π over ℝd by a product measure π⋆. When π is strongly log-concave and log-smooth, we provide (1) approximation rates certifying that π⋆ is close to the minimizer π⋆⋄ of the KL divergence over a \emph{polyhedral} set ⋄, and (2) an algorithm for minimizing KL(⋅‖π) over ⋄ with accelerated complexity O(κ√log(κd/ε2)), where κ is the condition number of π.more » « less
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