[R] Finding Optimum of Stochastic Function

ivo welch ivo.welch at anderson.ucla.edu
Mon May 18 23:47:49 CEST 2015

Could someone please point me to an optimizer for stochastic functions?
   (In http://cran.r-project.org/web/views/Optimization.html, I saw methods
that use random directions for deterministic functions, which is not the
kind of stochastic I need.)

For clarification, say I have an outcome function f(x), where x is a vector
of, say, 3 choices.  f(x) yields a simulated result that depends on random
draws.  That is, if I run it twice, it will give me different answers.  I
want to find the value of x that has the highest average f(x).

There are apparently well-defined algorithms, such as Robbins-Monro,
Kiefer-Wolfowitz, and Spall, although I don't know how they work nor do I
need to know much.  Presumably, a good algorithm knows not to draw too many
points at a given x too early (when far away from the optimum), but to
start more scattershot; and not to try to climb too aggressively.
Intuitively, I probably want to start from a point, draw in a cloud around
this point, and slowly sample-crawl into the direction where values tend to
be higher.  Ideally, the algorithm would try to solve an updatable
least-squares problem to determine its next sample.

Pointers appreciated.

regards, /iaw
Ivo Welch (ivo.welch at gmail.com)

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