Fast curvature matrix-vector products for second-order gradient descent

  • Authors:
  • Nicol N. Schraudolph

  • Affiliations:
  • IDSIA, Galleria 2, 6928 Manno, Switzerland, and Institute of Computational Science, ETH Zentrum, 8092 Zürich, Switzerland

  • Venue:
  • Neural Computation
  • Year:
  • 2002

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Abstract

We propose a generic method for iteratively approximating various second-order gradient steps--Newton, Gauss-Newton, Levenberg-Marquardt, and natural gradient--in linear time per iteration, using special curvature matrix-vector products that can be computed in O(n). Two recent acceleration techniques for on-line learning, matrix momentum and stochastic meta-descent (SMD), implement this approach. Since both were originally derived by very different routes, this offers fresh insight into their operation, resulting in further improvements to SMD.