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Parallel distributed block coordinate descent methods based on pairwise comparison oracle

Author

Listed:
  • Kota Matsui

    (Nagoya University)

  • Wataru Kumagai

    (Kanagawa University)

  • Takafumi Kanamori

    (Nagoya University)

Abstract

This paper provides a block coordinate descent algorithm to solve unconstrained optimization problems. Our algorithm uses only pairwise comparison of function values, which tells us only the order of function values over two points, and does not require computation of a function value itself or a gradient. Our algorithm iterates two steps: the direction estimate step and the search step. In the direction estimate step, a Newton-type search direction is estimated through a block coordinate descent-based computation method with the pairwise comparison. In the search step, a numerical solution is updated along the estimated direction. The computation in the direction estimate step can be easily parallelized, and thus, the algorithm works efficiently to find the minimizer of the objective function. Also, we theoretically derive an upper bound of the convergence rate for our algorithm and show that our algorithm achieves the optimal query complexity for specific cases. In numerical experiments, we show that our method efficiently finds the optimal solution compared to some existing methods based on the pairwise comparison.

Suggested Citation

  • Kota Matsui & Wataru Kumagai & Takafumi Kanamori, 2017. "Parallel distributed block coordinate descent methods based on pairwise comparison oracle," Journal of Global Optimization, Springer, vol. 69(1), pages 1-21, September.
  • Handle: RePEc:spr:jglopt:v:69:y:2017:i:1:d:10.1007_s10898-016-0465-x
    DOI: 10.1007/s10898-016-0465-x
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    References listed on IDEAS

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    1. Fuchang Gao & Lixing Han, 2012. "Implementing the Nelder-Mead simplex algorithm with adaptive parameters," Computational Optimization and Applications, Springer, vol. 51(1), pages 259-277, January.
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