On Fri, Aug 29, 2008 at 12:23 AM, bryan cole <bryan.cole@teraview.com> wrote:
Hi,
I'll looking for a bit of guidance as to what sort of algorithm is most appropriate/efficient for finding the local maximum of a function (in 2 dimensions), where each function evaluation is 1) noisy and 2) expensive/slow to evaluate.
Do you have a formula for the function f ? If what you have is only noisy observations of f(x), without knowing f, that's basically what stochastic approximation is about: you have a big literature about this kind of problems. The first article is the one introducing Robbins-Monro algorithm: Robbins, H. and Monro, S. "A Stochastic Approximation Method." Ann. Math. Stat. 22, 400-407, 1951. A recent book covering the field is the Kushner and Yin book: http://www.springer.com/math/probability/book/978-0-387-00894-3?cm_mmc=Googl... The problem of those algorithms is that they are hard to implement in python, because of their recursive nature, hence non vectorizable. If your function/observation is hard to compute, it may not be a big problem, though. cheers, David