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On Matching Pursuit and Coordinate Descent
Francesco Locatello · Anant Raj · Sai Praneeth Reddy Karimireddy · Gunnar Ratsch · Bernhard Schölkopf · Sebastian Stich · Martin Jaggi

Fri Jul 13 02:40 AM -- 02:50 AM (PDT) @ A9
Two popular examples of first-order optimization methods over linear spaces are coordinate descent and matching pursuit algorithms, with their randomized variants. While the former targets the optimization by moving along coordinates, the latter considers a generalized notion of directions. Exploiting the connection between the two algorithms, we present a unified analysis of both, providing affine invariant sublinear $O(1/t)$ rates on smooth objectives and linear convergence on strongly convex objectives. As a byproduct of our affine invariant analysis of matching pursuit, our rates for steepest coordinate descent are the tightest known. Furthermore, we show the first accelerated convergence rate $O(1/t^2)$ for matching pursuit and steepest coordinate descent on convex objectives.

Author Information

Francesco Locatello (MPI - ETH)
Anant Raj (Max-Planck Institute for Intelligent Systems)

Marie-Curie Fellow

Sai Praneeth Reddy Karimireddy (EPFL)
Gunnar Ratsch (ETH Zurich)
Bernhard Schölkopf (MPI for Intelligent Systems Tübingen, Germany)

Bernhard Scholkopf received degrees in mathematics (London) and physics (Tubingen), and a doctorate in computer science from the Technical University Berlin. He has researched at AT&T Bell Labs, at GMD FIRST, Berlin, at the Australian National University, Canberra, and at Microsoft Research Cambridge (UK). In 2001, he was appointed scientific member of the Max Planck Society and director at the MPI for Biological Cybernetics; in 2010 he founded the Max Planck Institute for Intelligent Systems. For further information, see www.kyb.tuebingen.mpg.de/~bs.

Sebastian Stich (EPFL)
Martin Jaggi (EPFL)

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