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The existing machine learning algorithms for minimizing the convex functionover a closed convex set suffer from slow convergence because their learningrates must be determined before running them. This paper proposes two machinelearning algorithms incorporating the line search method, which automaticallyand algorithmically finds appropriate learning rates at run-time. One algorithmis based on the incremental subgradient algorithm, which sequentially andcyclically uses each of the parts of the objective function; the other is basedon the parallel subgradient algorithm, which uses parts independently inparallel. These algorithms can be applied to constrained nonsmooth convexoptimization problems appearing in tasks of learning support vector machineswithout adjusting the learning rates precisely. The proposed line search methodcan determine learning rates to satisfy weaker conditions than the ones used inthe existing machine learning algorithms. This implies that the two algorithmsare generalizations of the existing incremental and parallel subgradientalgorithms for solving constrained nonsmooth convex optimization problems. Weshow that they generate sequences that converge to a solution of theconstrained nonsmooth convex optimization problem under certain conditions. Themain contribution of this paper is the provision of three kinds of experimentshowing that the two algorithms can solve concrete experimental problems fasterthan the existing algorithms. First, we show that the proposed algorithms haveperformance advantages over the existing ones in solving a test problem.Second, we compare the proposed algorithms with a different algorithm Pegasos,which is designed to learn with a support vector machine efficiently, in termsof prediction accuracy, value of the objective function, and computationaltime. Finally, we use...

Incremental and Parallel Machine Learning Algorithms with Automated Learning Rate Adjustments