Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Linearly Convergent Douglas-Rachford Splitting Solver for Markovian
  Information-Theoretic Optimization Problems   In this work, we propose solving the Information bottleneck (IB) and Privacy
Funnel (PF) problems with Douglas-Rachford Splitting methods (DRS). We study a
general Markovian information-theoretic Lagrangian that formulates the IB and
PF problems into a convex-weakly convex pair of functions in a unified
framework. Exploiting the recent non-convex convergence analysis for splitting
methods, we prove the linear convergence of the proposed algorithms using the
Kurdyka-{\L}ojasiewicz inequality. Moreover, our analysis is beyond IB and PF
and applies to any convex-weakly convex pair objectives. Based on the results,
we develop two types of IB solvers, with one improves the performance of
convergence over existing solvers while the other is linearly convergent
independent to the relevance-compression trade-off, and a class of PF solvers
that can handle both random and deterministic mappings. Empirically, we
evaluate the proposed DRS solvers for both the IB and PF problems with our
gradient-descent-based implementation. For IB, the proposed solvers result in
solutions that are comparable to those obtained through the
Blahut-Arimoto-based benchmark and is convergent for a wider range of the
penalty coefficient than existing solvers. For PF, our non-greedy solvers can
explore the information plane better than the clustering-based greedy solvers.

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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-th
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
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The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga