Healing Truncation Bias: Self-Weighted Truncation Framework for Dual Averaging

Abstract

We propose a new truncation framework for online supervised learning. Learning a compact predictive model in an online setting has recently attracted a great deal of attention. The combination of online learning with sparsity-inducing regularization enables faster learning with a smaller memory space than a conventional learning framework. However, a simple combination of these triggers the truncation of weights whose corresponding features rarely appear, even if these features are crucial for prediction. Furthermore, it is difficult to emphasize these features in advance while preserving the advantages of online learning. We develop an extensional truncation framework to Dual Averaging, which retains rarely occurring but informative features. Our proposed framework integrates information on all previous sub gradients of the loss functions into a regularization term. Our enhancement of a conventional L1-regularization accomplishes the automatic adjustment of each feature's truncations. This extension enables us to identify and retain rare but informative features without preprocessing. In addition, our framework achieves the same computational complexity and regret bound as standard Dual Averaging. Experiments demonstrated that our framework outperforms other sparse online learning algorithms.