Bridging the Gap between Constant Step Size Stochastic Gradient Descent and Markov Chains

20 Jul 2017 Aymeric Dieuleveut Alain Durmus Francis Bach

We consider the minimization of an objective function given access to unbiased estimates of its gradient through stochastic gradient descent (SGD) with constant step-size. While the detailed analysis was only performed for quadratic functions, we provide an explicit asymptotic expansion of the moments of the averaged SGD iterates that outlines the dependence on initial conditions, the effect of noise and the step-size, as well as the lack of convergence in the general (non-quadratic) case... (read more)

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METHOD TYPE
SGD
Stochastic Optimization