I have a rather straight-forward algorithm for finding the maximum-likelihood parameter of a probability distribution using sub-sampling. I'm fairly confident this algorithm is not novel and was hoping someone might recognize it from the following description. I will use biased coin-flipping as the example, as it is probably the easiest to understand.

Assume we have observed $$N$$ coin flips. Call the set of observations $$S$$. We would like to compute an approximation the Bernoulli parameter $$p^*$$ which maximizes the likelihood of the observed data without overfitting.

1. Select a trial value $$p$$ for the parameter.
2. Uniformly randomly select $$n$$ samples from $$S$$. Call this sub-sampled set $$s$$.
3. Compute the maximum-likelihood parameter $$\theta(s)$$ for the sub-sample.
4. Using $$\lVert p - \theta(s) \rVert^2$$ (or similar) as error, compute one step of gradient-descent to update $$p$$
5. Repeat steps 2-4 until desired convergence

Can anyone recognize this as a specific case of a well-known algorithm?