Minimum description length (MDL) regularization for online learning

An approach inspired by the Minimum Description Length (MDL) principle is proposed for adaptively selecting features during online learning based on their usefulness in improving the objective. The approach eliminates noisy or useless features from the optimization process, leading to improved loss. Several algorithmic variations on the approach are presented. They are based on using a Bayesian mixture in each of the dimensions of the feature space. By utilizing the MDL principle, the mixture reduces the dimensionality of the feature space to its subspace with the lowest loss. Bounds on the loss, derived, show that the loss for that subspace is essentially achieved. The approach can be tuned for trading off between model size and the loss incurred. Empirical results on large scale real-world systems demonstrate how it improves such tradeoffs. Huge model size reductions can be achieved with no loss in performance relative to standard techniques, while moderate loss improvements (translating to large regret improvements) are achieved with moderate size reductions. The results also demonstrate that overfitting is eliminated by this approach.