2009/09/07 by Ankan Saha, Xinhua Zhang, Saha, Ankan +3
Computer Science · Engineering · #Advanced Multi-Objective Optimization Algorithms #Artificial Intelligence (cs.AI) #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning and Algorithms #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.0909.1334
openalex publication_date 2009/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Regularized risk minimization with the binary hinge loss and its variants lies at the heart of many machine learning problems. Bundle methods for regularized risk minimization (BMRM) and the closely related SVMStruct are considered the best general purpose solvers to tackle this problem. It was recently shown that BMRM requires O(1/ε) iterations to converge to an ε accurate solution. In the first part of the paper we use the Hadamard matrix to construct a regularized risk minimization problem and show that these rates cannot be improved. We then show how one can exploit the structure of the objective function to devise an algorithm for the binary hinge loss which converges to an ε accurate solution in O(1/√ε) iterations.