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Volumn 24, Issue 4, 2014, Pages 2057-2075

A proximal stochastic gradient method with progressive variance reduction

Author keywords

Proximal mapping; Stochastic gradient method; Variance reduction

Indexed keywords

ARTIFICIAL INTELLIGENCE; FUNCTIONS; GRADIENT METHODS; LEARNING SYSTEMS; MAPPING;

EID: 84919793228     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/140961791     Document Type: Article
Times cited : (725)

References (35)
  • 1
    • 85014561619 scopus 로고    scopus 로고
    • A fast iterative shrinkage-threshold algorithm for linear inverse problems
    • A. BECK AND M. TEBOULLE, A fast iterative shrinkage-threshold algorithm for linear inverse problems, SIAM J. Imaging Sci., 2(2009), pp. 183-202.
    • (2009) SIAM J. Imaging Sci. , vol.2 , pp. 183-202
    • Beck, A.1    Teboulle, M.2
  • 3
    • 81155150371 scopus 로고    scopus 로고
    • Incremental proximal methods for large scale convex optimization
    • D. P. BERTSEKAS, Incremental proximal methods for large scale convex optimization, Math. Program. Ser. B, 129(2011), pp. 163-195.
    • (2011) Math. Program. Ser. B , vol.129 , pp. 163-195
    • Bertsekas, D.P.1
  • 5
    • 39449100600 scopus 로고    scopus 로고
    • A convergent incremental gradient method with a constant step size
    • D. BLATT, A. O. HERO, AND H. GAUCHMAN, A convergent incremental gradient method with a constant step size, SIAM J. Optim., 18(2007), pp. 29-51.
    • (2007) SIAM J. Optim. , vol.18 , pp. 29-51
    • Blatt, D.1    Hero, A.O.2    Gauchman, H.3
  • 6
    • 84865685824 scopus 로고    scopus 로고
    • Sample size selection in optimization methods for machine learning
    • R. H. BYRD, G. M. CHIN, J. NOCEDAL, AND Y. WU, Sample size selection in optimization methods for machine learning, Math. Program. Ser. B, 134(2012), pp. 127-155.
    • (2012) Math. Program. Ser. B , vol.134 , pp. 127-155
    • Byrd, R.H.1    Chin, G.M.2    Nocedal, J.3    Wu, Y.4
  • 7
    • 0031496462 scopus 로고    scopus 로고
    • Convergence rates in forward-backward splitting
    • G. H.-G. CHEN AND R. T. ROCKAFELLAR, Convergence rates in forward-backward splitting, SIAM J. Optim., 7(1997), pp. 421-444.
    • (1997) SIAM J. Optim. , vol.7 , pp. 421-444
    • Chen, G.H.-G.1    Rockafellar, R.T.2
  • 8
    • 75249102673 scopus 로고    scopus 로고
    • Efficient online and batch learning using forward backward splitting
    • J. DUCHI AND Y. SINGER, Efficient online and batch learning using forward backward splitting, J. Mach. Learn. Res., 10(2009), pp. 2873-2898.
    • (2009) J. Mach. Learn. Res. , vol.10 , pp. 2873-2898
    • Duchi, J.1    Singer, Y.2
  • 11
    • 84877784292 scopus 로고    scopus 로고
    • Hybrid deterministic-stochastic methods for data fitting
    • M. P. FRIEDLANDER AND M. SCHMIDT, Hybrid deterministic-stochastic methods for data fitting, SIAM J. Sci. Comput., 34(2012), pp. 1380-1405.
    • (2012) SIAM J. Sci. Comput. , vol.34 , pp. 1380-1405
    • Friedlander, M.P.1    Schmidt, M.2
  • 14
    • 77956508892 scopus 로고    scopus 로고
    • Accelerated gradient methods for stochastic optimization and online learning
    • MIT Press, Cambridge, MA
    • C. HU, J. T. KWOK, AND W. PAN, Accelerated gradient methods for stochastic optimization and online learning, in Adv. Neural Inf. Process. Syst. 22, MIT Press, Cambridge, MA, 2009, pp. 781-789.
    • (2009) Adv. Neural Inf. Process. Syst , vol.22 , pp. 781-789
    • Hu, C.1    Kwok, J.T.2    Pan, W.3
  • 15
    • 84898963415 scopus 로고    scopus 로고
    • Accelerating stochastic gradient descent using predictive variance Reduction
    • MIT Press, Cambridge, MA
    • R. JOHNSON AND T. ZHANG, Accelerating stochastic gradient descent using predictive variance Reduction, in Adv. Neural Inf. Process. Syst. 26, MIT Press, Cambridge, MA, 2013, pp. 315-323.
    • (2013) Adv. Neural Inf. Process. Syst , vol.26 , pp. 315-323
    • Johnson, R.1    Zhang, T.2
  • 17
    • 64149115569 scopus 로고    scopus 로고
    • Sparse online learning via truncated gradient
    • J. LANGFORD, L. LI, AND T. ZHANG, Sparse online learning via truncated gradient, J. Mach. Learn. Res., 10(2009), pp. 777-801.
    • (2009) J. Mach. Learn. Res. , vol.10 , pp. 777-801
    • Langford, J.1    Li, L.2    Zhang, T.3
  • 19
    • 84876811202 scopus 로고    scopus 로고
    • RCV 1: A new benchmark collection for text categorization research
    • D. D. LEWIS, Y. YANG, T. ROSE, AND F. LI, RCV 1: A new benchmark collection for text categorization research, J. Mach. Learn. Res., 5(2004), pp. 361-397.
    • (2004) J. Mach. Learn. Res. , vol.5 , pp. 361-397
    • Lewis, D.D.1    Yang, Y.2    Rose, T.3    Li, F.4
  • 20
    • 0000345334 scopus 로고
    • Splitting algorithms for the sum of two nonlinear operators
    • P.-L. LIONS AND B. MERCIER, Splitting algorithms for the sum of two nonlinear operators, SIAM J. Numer. Anal., 16(1979), pp. 964-979.
    • (1979) SIAM J. Numer. Anal. , vol.16 , pp. 964-979
    • Lions, P.-L.1    Mercier, B.2
  • 21
    • 84898988901 scopus 로고    scopus 로고
    • Mixed optimization for smooth functions
    • MIT Press, Cambridge, MA
    • M. MAHDAVI, L. ZHANG, AND R. JIN, Mixed optimization for smooth functions, in Adv. Neural Inf. Process. Syst. 26, MIT Press, Cambridge, MA, 2013, pp. 674-682.
    • (2013) Adv. Neural Inf. Process. Syst , vol.26 , pp. 674-682
    • Mahdavi, M.1    Zhang, L.2    Jin, R.3
  • 24
    • 84865692149 scopus 로고    scopus 로고
    • Efficiency of coordinate descent methods on huge-scale optimization problems
    • Y. NESTEROV, Efficiency of coordinate descent methods on huge-scale optimization problems, SIAM J. Optim., 22(2012), pp. 341-362.
    • (2012) SIAM J. Optim. , vol.22 , pp. 341-362
    • Nesterov, Y.1
  • 25
    • 84879800501 scopus 로고    scopus 로고
    • Gradient methods for minimizing composite functions
    • YU. NESTEROV, Gradient methods for minimizing composite functions, Math. Program. Ser. B, 140(2013), pp. 125-161.
    • (2013) Math. Program. Ser. B , vol.140 , pp. 125-161
    • Nesterov, Yu.1
  • 26
    • 84897116612 scopus 로고    scopus 로고
    • Iteration complexity of randomized block-coordinate descent methods for minimizing a composite function
    • P. RICHTÁRIK AND M. TAKÁČ, Iteration complexity of randomized block-coordinate descent methods for minimizing a composite function, Math. Program., 144(2014), pp. 1-38.
    • (2014) Math. Program. , vol.144 , pp. 1-38
    • Richtárik, P.1    Takáč, M.2
  • 27
    • 0004267646 scopus 로고
    • Princeton University Press, Princeton, NJ
    • R. T. ROCKAFELLAR, Convex Analysis, Princeton University Press, Princeton, NJ, 1970.
    • (1970) Convex Analysis
    • Rockafellar, R.T.1
  • 28
    • 84877725219 scopus 로고    scopus 로고
    • A stochastic gradient method with an exponential convergence rate for finite training sets
    • MIT Press, Cambridge, MA
    • N. LE ROUX, M. SCHMIDT, AND F. BACH, A stochastic gradient method with an exponential convergence rate for finite training sets, in Adv. Neural Inf. Process. Syst. 25, MIT Press, Cambridge, MA, 2012, pp. 2672-2680.
    • (2012) Adv. Neural Inf. Process. Syst , vol.25 , pp. 2672-2680
    • Le Roux, N.1    Schmidt, M.2    Bach, F.3
  • 31
    • 84875134236 scopus 로고    scopus 로고
    • Stochastic dual coordinate ascent methods for regularized loss minimization
    • S. SHALEV-SHWARTZ AND T. ZHANG, Stochastic dual coordinate ascent methods for regularized loss minimization, J. Mach. Learn. Res., 14(2013), pp. 567-599.
    • (2013) J. Mach. Learn. Res. , vol.14 , pp. 567-599
    • Shalev-Shwartz, S.1    Zhang, T.2
  • 32
    • 0033884548 scopus 로고    scopus 로고
    • A modified forward-backward splitting method for maximal monotone mappings
    • P. TSENG, A modified forward-backward splitting method for maximal monotone mappings, SIAM J. Control Optim., 38(2000), pp. 431-446.
    • (2000) SIAM J. Control Optim. , vol.38 , pp. 431-446
    • Tseng, P.1
  • 33
    • 78649396336 scopus 로고    scopus 로고
    • Dual averaging methods for regularized stochastic learning and online optimization
    • L. XIAO, Dual averaging methods for regularized stochastic learning and online optimization, J. Mach. Learn. Res., 11(2010), pp. 2534-2596.
    • (2010) J. Mach. Learn. Res. , vol.11 , pp. 2534-2596
    • Xiao, L.1
  • 34
    • 84898971059 scopus 로고    scopus 로고
    • Linear convergence with condition number independent access of full gradients
    • MIT Press, Cambridge, MA
    • L. ZHANG, M. MAHDAVI, AND R. JIN, Linear convergence with condition number independent access of full gradients, in Adv. Neural Inf. Process. Syst. 26, MIT Press, Cambridge, MA, 2013, pp. 980-988.
    • (2013) Adv. Neural Inf. Process. Syst , vol.26 , pp. 980-988
    • Zhang, L.1    Mahdavi, M.2    Jin, R.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.