Pegasos: primal estimated sub-gradient solver for SVM. We describe and analyze a simple and effective stochastic sub-gradient descent algorithm for solving the optimization problem cast by Support Vector Machines (SVM). We prove that the number of iterations required to obtain a solution of accuracy ϵ is O (1/ϵ) , where each iteration operates on a single training example. In contrast, previous analyses of stochastic gradient descent methods for SVMs require Ω(1/ϵ2) iterations. As in previously devised SVM solvers, the number of iterations also scales linearly with 1/λ, where λ is the regularization parameter of SVM. For a linear kernel, the total run-time of our method is O (d/(λϵ)) , where d is a bound on the number of non-zero features in each example. Since the run-time does not depend directly on the size of the training set, the resulting algorithm is especially suited for learning from large datasets. Our approach also extends to non-linear kernels while working solely on the primal objective function, though in this case the runtime does depend linearly on the training set size. Our algorithm is particularly well suited for large text classification problems, where we demonstrate an order-of-magnitude speedup over previous SVM learning methods

References in zbMATH (referenced in 84 articles , 1 standard article )

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  1. Iiduka, Hideaki: Decentralized hierarchical constrained convex optimization (2020)
  2. Jiang, Wei; Siddiqui, Sauleh: Hyper-parameter optimization for support vector machines using stochastic gradient descent and dual coordinate descent (2020)
  3. Lan, Guanghui; Zhou, Zhiqiang: Algorithms for stochastic optimization with function or expectation constraints (2020)
  4. Ahookhosh, Masoud; Neumaier, Arnold: An optimal subgradient algorithm with subspace search for costly convex optimization problems (2019)
  5. Asi, Hilal; Duchi, John C.: Stochastic (approximate) proximal point methods: convergence, optimality, and adaptivity (2019)
  6. Grimmer, Benjamin: Convergence rates for deterministic and stochastic subgradient methods without Lipschitz continuity (2019)
  7. Guo, Zheng-Chu; Shi, Lei: Fast and strong convergence of online learning algorithms (2019)
  8. Li, Ningning; Xue, Dan; Sun, Wenyu; Wang, Jing: A stochastic trust region method for unconstrained optimization problems (2019)
  9. Shahparast, Homeira; Mansoori, Eghbal G.: Developing an online general type-2 fuzzy classifier using evolving type-1 rules (2019)
  10. Aggarwal, Charu C.: Neural networks and deep learning. A textbook (2018)
  11. Aggarwal, Charu C.: Machine learning for text (2018)
  12. Bottou, Léon; Curtis, Frank E.; Nocedal, Jorge: Optimization methods for large-scale machine learning (2018)
  13. Csiba, Dominik; Richtárik, Peter: Importance sampling for minibatches (2018)
  14. Horn, Daniel; Demircioğlu, Aydın; Bischl, Bernd; Glasmachers, Tobias; Weihs, Claus: A comparative study on large scale kernelized support vector machines (2018)
  15. Lei, Yunwen; Shi, Lei; Guo, Zheng-Chu: Convergence of unregularized online learning algorithms (2018)
  16. Manno, Andrea; Palagi, Laura; Sagratella, Simone: Parallel decomposition methods for linearly constrained problems subject to simple bound with application to the SVMs training (2018)
  17. Nguyen, Hien D.; Jones, Andrew T.; McLachlan, Geoffrey J.: Stream-suitable optimization algorithms for some soft-margin support vector machine variants (2018)
  18. Piccialli, Veronica; Sciandrone, Marco: Nonlinear optimization and support vector machines (2018)
  19. Tappenden, Rachael; Takáč, Martin; Richtárik, Peter: On the complexity of parallel coordinate descent (2018)
  20. Van der Laan, Mark J.; Rose, Sherri: Targeted learning in data science. Causal inference for complex longitudinal studies (2018)

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