Learning with Smooth Hinge Losses
This work addresses a bottleneck in SVM optimization for machine learning practitioners, offering incremental improvements in convergence rates.
The paper tackles the non-smoothness of the Hinge loss in SVMs by introducing two smooth Hinge losses, leading to quadratically convergent algorithms with experiments showing effectiveness in text classification tasks.
Due to the non-smoothness of the Hinge loss in SVM, it is difficult to obtain a faster convergence rate with modern optimization algorithms. In this paper, we introduce two smooth Hinge losses $ψ_G(α;σ)$ and $ψ_M(α;σ)$ which are infinitely differentiable and converge to the Hinge loss uniformly in $α$ as $σ$ tends to $0$. By replacing the Hinge loss with these two smooth Hinge losses, we obtain two smooth support vector machines(SSVMs), respectively. Solving the SSVMs with the Trust Region Newton method (TRON) leads to two quadratically convergent algorithms. Experiments in text classification tasks show that the proposed SSVMs are effective in real-world applications. We also introduce a general smooth convex loss function to unify several commonly-used convex loss functions in machine learning. The general framework provides smooth approximation functions to non-smooth convex loss functions, which can be used to obtain smooth models that can be solved with faster convergent optimization algorithms.