Sketched follow-the-regularized-leader for online factorization machine

Factorization Machine (FM) is a supervised machine learning model for feature engineering, which is widely used in many real-world applications. In this paper, we consider the case that the data samples arrive sequentially. The existing convex formulation for online FM has the strong theoretical guarantee and stable performance in practice, but the computational cost is typically expensive when the data is high-dimensional. To address this weakness, we devise a novel online learning algorithm called Sketched Follow-The-Regularizer-Leader (SFTRL). SFTRL presents the parameters of FM implicitly by maintaining low-rank matrices and updates the parameters via sketching. More specifically, we propose Generalized Frequent Directions to approximate indefinite symmetric matrices in a streaming way, making that the sum of historical gradients for FM could be estimated with tighter error bound efficiently. With mild assumptions, we prove that the regret bound of SFTRL is close to that of the standard FTRL. Experimental results show that SFTRL has better prediction quality than the state-of-the-art online FM algorithms in much lower time and space complexities.