Efficient Learning using Forward-Backward Splitting
published: Jan. 19, 2010, recorded: December 2009, views: 357
Report a problem or upload filesIf you have found a problem with this lecture or would like to send us extra material, articles, exercises, etc., please use our ticket system to describe your request and upload the data.
Enter your e-mail into the 'Cc' field, and we will keep you updated with your request's status.
We describe, analyze, and experiment with a new framework for empirical loss minimization with regularization. Our algorithmic framework alternates between two phases. On each iteration we first perform an unconstrained gradient descent step. We then cast and solve an instantaneous optimization problem that trades off minimization of a regularization term while keeping close proximity to the result of the first phase. This yields a simple yet effective algorithm for both batch penalized risk minimization and online learning. Furthermore, the two phase approach enables sparse solutions when used in conjunction with regularization functions that promote sparsity, such as ℓ1. We derive concrete and very simple algorithms for minimization of loss functions with ℓ1, ℓ2, ℓ2 2, and ℓ∞ regularization. We also show how to construct efficient algorithms for mixed-norm ℓ1/ℓq regularization. We further extend the algorithms and give efficient implementations for very high-dimensional data with sparsity. We demonstrate the potential of the proposed framework in experiments with synthetic and natural datasets.
Link this pageWould you like to put a link to this lecture on your homepage?
Go ahead! Copy the HTML snippet !