I want to find the argument of a function for which it is minimal. The function is expected to be convex but I cannot evaluate it exactly so I have to deal with the fact that there's noise on top. The noise is purely statistical and I roughly know its magnitude. Essentially, I run a Monte Carlo simulation for each evaluation of the function, so I can even control the error.
I don't need to know the minimum with too much precision. The higher the value of the function, the larger the yield of the simulation.
Thus my requirements are:
- really costly function evaluation
- 1D function
- no derivative available
- convexity up to statistical errors of know magnitude
Also, it's rather important that the whole procedure is not terribly complicated. I'm aware of this thread:
but that's just a little too much. I need something simple, yet reliable. I tried a simple bisection scheme but that really didn't handle the noise too well.