Projection Dual Averaging Based Second-order Online Learning

• Published in: 2022 IEEE International Conference on Data Mining (ICDM) pp. 51 - 60
• Main Authors: Chen, Zhong, Zhan, Huixin, Sheng, Victor, Edwards, Andrea, Zhang, Kun
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.11.2022
• Subjects: Classification algorithms; Computational efficiency; Costs; data streams; Hessian sketch; Learning systems; projection dual averaging; regret bound; second-order online learning; Sensitivity analysis; Solids; Task analysis
• ISSN: 2374-8486
• DOI: 10.1109/ICDM54844.2022.00015

Most existing online learning methods focus on mining ever-evolving streaming data based on the principle of first-order optimization. However, one drawback of these methods is the slow convergence rate in each iteration, resulting in sub-optimal solutions and deteriorated performance. Second-order methods, while are able to provide faster convergence, have been under-studied due to the high cost of computing the curvature information. To address this problem, in this paper, we develop a second-order projection dual averaging based online learning (SPDA) method to effectively handle high-throughput streaming data. By fully exploiting the regularized dual averaging optimization, the second-order information, and an optimal projection operator, SPDA converges fast with fairly optimal solutions. Two speed-up versions of SPDA, i.e., SPDA-diag and SPDA-sketch, are developed via the diagonal operator and Hessian sketch, respectively. Theoretical derivations on the regret bound of SPDA establish a solid convergence guarantee for this method. Extensive experiments demonstrate the efficacy of the proposed algorithms on large-scale online learning tasks, such as online binary and multi-class classification and online anomaly detection, shedding light on their potential wide applications.