2018/09/25 by Chaobing Song, Ji Liu, Song, Chaobing +7
Computer Science · #FOS: Computer and information sciences #Face and Expression Recognition #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning and Algorithms #Stochastic Gradient Optimization Techniques
paper · pdf · doi:10.48550/arxiv.1809.09350
openalex publication_date 2018/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Regularized online learning is widely used in machine learning applications. In online learning, performing exact minimization (i.e., implicit update) is known to be beneficial to the numerical stability and structure of solution. In this paper we study a class of regularized online algorithms without linearizing the loss function or the regularizer, which we call fully implicit online learning (FIOL). We show that for arbitrary Bregman divergence, FIOL has the O(√(T)) regret for general convex setting and O(log T) regret for strongly convex setting, and the regret has an one-step improvement effect because it avoids the approximation error of linearization. Then we propose efficient algorithms to solve the subproblem of FIOL. We show that even if the solution of the subproblem has no closed form, it can be solved with complexity comparable to the linearized online algoritms. Experiments validate the proposed approaches.