  We present algorithms for efficiently learning regularizers that improve
generalization. Our approach is based on the insight that regularizers can be
viewed as upper bounds on the generalization gap, and that reducing the slack
in the bound can improve performance on test data. For a broad class of
regularizers, the hyperparameters that give the best upper bound can be
computed using linear programming. Under certain Bayesian assumptions, solving
the LP lets us "jump" to the optimal hyperparameters given very limited data.
This suggests a natural algorithm for tuning regularization hyperparameters,
which we show to be effective on both real and synthetic data.
