Abstract

We propose a general method called truncated gradient to induce sparsity in the weights of online learning algorithms with convex loss functions. This method has several essential properties:

1. The degree of sparsity is continuous—a parameter controls the rate of sparsification from no sparsification to total sparsification.
2. The approach is theoretically motivated, and an instance of it can be regarded as an online counterpart of the popular L1-regularization method in the batch setting. We prove that small rates of sparsification result in only small additional regret with respect to typical online-learning guarantees.
3. The approach works well empirically. We apply the approach to several data sets and find for data sets with large numbers of features, substantial sparsity is discoverable.