求解L1正则化L2损失支持向量机问题的多层随机坐标下降算法

A multi-level randomized coordinate descent algorithm for solving L1-regularized L2-loss support vector machines problems

针对L1正则化L2损失支持向量机问题,基于多层优化思想,提出一种求解该问题的多层随机坐标下降算法。该算法有如下特点:若满足粗糙条件,则将求得的粗糙模型的解用于计算精细模型的搜索方向,再利用Armijo线搜索求解步长,从而得到下一个迭代点,否则,利用随机坐标下降算法求解精细模型的下一个迭代点。数值实验结果表明,多层随机坐标下降算法求解L1正则化L2损失支持向量机问题是有效的。

In order to solve the L1-regularized L2-loss support vector machines problems,a multi-level randomized coordinate descent algorithm(MRCDA)based on the idea of multi-level optimization is proposed.The algorithm has the following characteristics:if the coarse condition is met,the solution obtained by the coarse model is used to calculate the search direction of the fine model,and the Armijo line search is used to obtain the step size,so as to get the next iterative point,otherwise,use randomized coordinate descent algorithm to solve the fine model to find the next iterative point.Finally,the corresponding numerical experiments show that the multi-level randomized coordinate descent algorithm is effective to solve the L1-regularized L2-loss support vector machines problems.