closing the convergence gap of sgd without replacement
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Closing the convergence gap of SGD without replacement Shashank Rajput, Anant Gupta, Dimitris Papailiopoulos <latexit

  1. Closing the convergence gap of SGD without replacement Shashank Rajput, Anant Gupta, Dimitris Papailiopoulos

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sha1_base64="Mwv+2sFCgxVJoPAQ2pdYIYCMGM=">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</latexit> Stochastic Gradient Descent (SGD) P n • F ( x ) := 1 Sampling with replacement Problem : min i =1 f i ( x ) n x • Algorithm: 1. At each iteration, sample f i randomly from { f 1 , . . . , f n } 2. x t +1 := x t � α r f i ( x t ) , α is the step size 3. Repeat for T iterations • SGD with replacement is theoretically well understood However, in practice we sample without replacement

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