Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Wasserstein Proximal Gradient Algorithm   Wasserstein gradient flows are continuous time dynamics that define curves of
steepest descent to minimize an objective function over the space of
probability measures (i.e., the Wasserstein space). This objective is typically
a divergence w.r.t. a fixed target distribution. In recent years, these
continuous time dynamics have been used to study the convergence of machine
learning algorithms aiming at approximating a probability distribution.
However, the discrete-time behavior of these algorithms might differ from the
continuous time dynamics. Besides, although discretized gradient flows have
been proposed in the literature, little is known about their minimization
power. In this work, we propose a Forward Backward (FB) discretization scheme
that can tackle the case where the objective function is the sum of a smooth
and a nonsmooth geodesically convex terms. Using techniques from convex
optimization and optimal transport, we analyze the FB scheme as a minimization
algorithm on the Wasserstein space. More precisely, we show under mild
assumptions that the FB scheme has convergence guarantees similar to the
proximal gradient algorithm in Euclidean spaces.

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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ph
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: physics
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: econ
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The categories of this paper are: chao-dyn