Further Bernoulli factories

Yesterday, Andrew Thomas and José Blanchet posted a note on the Bernouilli factory on arXiv. This short paper links with the recent paper of Flegal and Herbei I commented earlier. Considering the special target

$f(p) = \min(cp, 1-\epsilon)$

Thomas and Blanchet develop an elaborate scheme of cascading envelopes that converge to f from above. Their paper is very clear to read, the connection with the Bernstein polynomials is well-explained, the R code is available, and the ten-fold gain over the Flegal and Herbei version is impressive. However, I feel the note in its current state could be improved into a deeper paper by detailing the extension to other functions than the above, by studying further the associated computing time, and by exhibiting the limitations of the method…

Other recent arXiv postings of interest are

the latter being presumably related with the earlier arXiv description of their R package.