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The goal of the presentation is to describe practical stochastic gradient algorithms that process each training example only once, yet asymptotically match the performance of the true optimum. This statement needs, of course, to be made more precise. To achieve this, we'll review the works of Nevel'son and Has'minskij (1972), Fabian (1973, 1978), Murata & Amari (1998), Bottou & LeCun (2004), Polyak & Juditsky (1992), Wei Xu (2010), and Bach & Moulines (2011). We will then show how these ideas lead to practical algorithms that not only represent a new state of the art but are also arguably optimal.
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