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I guess convergence in general means it is in asymptotic sense but what does non-asymptotic convergence mean?. Can someone please explain with an example?

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  • $\begingroup$ Where did you find that term? Can you include some context? $\endgroup$ Commented Jun 10, 2020 at 14:52
  • $\begingroup$ Non-Asymptotic Analysis of Stochastic Approximation Algorithms for Machine Learning (papers.nips.cc/paper/…) @FedericoPoloni $\endgroup$ Commented Jun 10, 2020 at 15:29
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    $\begingroup$ Can you add some information from that paper to the question to provide context? Most people won't go and read that paper to understand your question. $\endgroup$
    – nicoguaro
    Commented Jun 10, 2020 at 15:50

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The authors provide bounds on various things as an explicit function of the iterate $n$, for a generic, but finite, $n$. These bounds apply for finite $n$, not only in the limit as $n \rightarrow \infty$, hence are non-asymptotic bounds.

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    $\begingroup$ With first order methods for optimization we don't typically run the optimization all the way to convergence but rather stop as soon as the solution is "good enough" This kind of analysis addresses the "good enough" problem. $\endgroup$ Commented Jun 10, 2020 at 18:32

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