Pages

Thursday, May 14, 2015

Newton Sketch: A Linear-time Optimization Algorithm with Linear-Quadratic Convergence

Another sketching algorithm using random projection this week:





Newton Sketch: A Linear-time Optimization Algorithm with Linear-Quadratic Convergence by Mert Pilanci, Martin J. Wainwright

We propose a randomized second-order method for optimization known as the Newton Sketch: it is based on performing an approximate Newton step using a randomly projected or sub-sampled Hessian. For self-concordant functions, we prove that the algorithm has super-linear convergence with exponentially high probability, with convergence and complexity guarantees that are independent of condition numbers and related problem-dependent quantities. Given a suitable initialization, similar guarantees also hold for strongly convex and smooth objectives without self-concordance. When implemented using randomized projections based on a sub-sampled Hadamard basis, the algorithm typically has substantially lower complexity than Newton's method. We also describe extensions of our methods to programs involving convex constraints that are equipped with self-concordant barriers. We discuss and illustrate applications to linear programs, quadratic programs with convex constraints, logistic regression and other generalized linear models, as well as semidefinite programs.
h/t Suresh for the find.
 
Join the CompressiveSensing subreddit or the Google+ Community and post there !
Liked this entry ? subscribe to Nuit Blanche's feed, there's more where that came from. You can also subscribe to Nuit Blanche by Email, explore the Big Picture in Compressive Sensing or the Matrix Factorization Jungle and join the conversations on compressive sensing, advanced matrix factorization and calibration issues on Linkedin.

1 comment:

  1. Hi,
    Do they have a MATLAB implementation?
    This is what I don't like on Arxiv, it doesn't allow spreading code.

    ReplyDelete