Look up this paper, and read it: Trevor Hastie, Saharon Rosset, Rob Tibshirani and Ji Zhu, The Entire Regularization Path for the Support Vector Machine, NIPS 2004
For a problem you are familiar with, apply their algorithm to construct the entire regularization path (you may use existing software, if you can find it). In particular, choose a regularizer value from the entire path. Does this give you better results in practice than the usual pastime of trying five regularizer values on a validation set? Why?
Note that I am encouraging clever experimentation here, rather than blank coding efficiency. In particular, is it worth knowing the entire regularization path?
This is a broad MP intended to be educational. I will grade on quality of experimental concept and of argument from data. Submit PDF's to me by April 11. Email them to me at daf@uiuc.edu, with "CS544" in the header