Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linearly Convergent Frank-Wolfe with Backtracking Line-Search   Structured constraints in Machine Learning have recently brought the
Frank-Wolfe (FW) family of algorithms back in the spotlight. While the
classical FW algorithm has poor local convergence properties, the Away-steps
and Pairwise FW variants have emerged as improved variants with faster
convergence. However, these improved variants suffer from two practical
limitations: they require at each iteration to solve a 1-dimensional
minimization problem to set the step-size and also require the Frank-Wolfe
linear subproblems to be solved exactly. In this paper, we propose variants of
Away-steps and Pairwise FW that lift both restrictions simultaneously. The
proposed methods set the step-size based on a sufficient decrease condition,
and do not require prior knowledge of the objective. Furthermore, they inherit
all the favorable convergence properties of the exact line-search version,
including linear convergence for strongly convex functions over polytopes.
Benchmarks on different machine learning problems illustrate large performance
gains of the proposed variants.

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The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: quant-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
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The categories of this paper are: cs
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The categories of this paper are: comp-gas
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The categories of this paper are: econ
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The categories of this paper are: nlin
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an