Alternating direction method of multipliers for regularized multiclass support vector machines
This work addresses a computational bottleneck for researchers and practitioners using regularized MSVMs, though it is incremental as it applies an existing optimization method to a known problem.
The paper tackles the computational expense of solving regularized multiclass support vector machines (MSVMs) by extending the alternating direction method of multipliers (ADMM) to these models, demonstrating high efficiency and accuracy in numerical experiments on synthetic and real data.
The support vector machine (SVM) was originally designed for binary classifications. A lot of effort has been put to generalize the binary SVM to multiclass SVM (MSVM) which are more complex problems. Initially, MSVMs were solved by considering their dual formulations which are quadratic programs and can be solved by standard second-order methods. However, the duals of MSVMs with regularizers are usually more difficult to formulate and computationally very expensive to solve. This paper focuses on several regularized MSVMs and extends the alternating direction method of multiplier (ADMM) to these MSVMs. Using a splitting technique, all considered MSVMs are written as two-block convex programs, for which the ADMM has global convergence guarantees. Numerical experiments on synthetic and real data demonstrate the high efficiency and accuracy of our algorithms.