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In a nutshell, stochastic approximation algorithms deal with a function of the form <math display="inline"> f(\theta) = \operatorname E_{\xi} [F(\theta,\xi)] </math>
which is the [[expected value]] of a function depending on a [[random variable]] <math display="inline">\xi </math>. The goal is to recover properties of such a function <math display="inline">f</math> without evaluating it directly. Instead, stochastic approximation algorithms use random samples of <math display="inline">F(\theta,\xi)</math> to efficiently approximate properties of <math display="inline">f</math> such as zeros or extrema.
Recently, stochastic approximations have found extensive applications in the fields of statistics and machine learning, especially in settings with [[big data]]. These applications range from [[stochastic optimization]] methods and algorithms, to online forms of the [[Expectation–maximization algorithm| EM algorithm]], reinforcement learning via [[Temporal difference learning|temporal differences]], and [[deep learning]], and others.<ref name=":1">{{cite journal |last1=Toulis |first1=Panos |first2=Edoardo |last2=Airoldi|title=Scalable estimation strategies based on stochastic approximations: classical results and new insights |journal=Statistics and Computing |volume=25 |issue=4 |year=2015 |pages=781–795|doi=10.1007/s11222-015-9560-y|pmid=26139959 |pmc=4484776 }}</ref>
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