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Stochastic gradient descent (often abbreviated SGD) is an iterative method for optimizing an objective function with suitable smoothness properties (e.g. differentiable or subdifferentiable). It can be regarded as a stochastic approximation of gradient descent optimization, since it replaces the actual gradient (calculated from the entire data set) by an estimate thereof (calculated from a randomly selected subset of the data). Especially in high-dimensional optimization problems this reduces the very high computational burden, achieving faster iterations in exchange for a lower convergence rate.^[1]

The basic idea behind stochastic approximation can be traced back to the Robbins–Monro algorithm of the 1950s. Today, stochastic gradient descent has become an important optimization method in machine learning.^[2]

^ Bottou, Léon; Bousquet, Olivier (2012). "The Tradeoffs of Large Scale Learning". In Sra, Suvrit; Nowozin, Sebastian; Wright, Stephen J. (eds.). Optimization for Machine Learning. Cambridge: MIT Press. pp. 351–368. ISBN 978-0-262-01646-9.
^ Bottou, Léon (1998). "Online Algorithms and Stochastic Approximations". Online Learning and Neural Networks. Cambridge University Press. ISBN 978-0-521-65263-6.