I have a system that takes in 'm' inputs and provides a cost value as an output. The system is a "black box" to me. The inputs can be varied and the corresponding output can be observed, however, I have no prior knowledge of the function that this box implements. Given that I can fiddle with the input values(all real valued), is there an algorithm or a learning based solution that can maximize the cost function in minimum number of iterations? I think this might be a well known problem, however, this genre is way beyond my ken and I am finding it difficult to frame the terms I should be googling for. A link or mention of the name of the algorithm or a short description of the solution would be appreciated.
If don't know anything about the function, then your problam is practically unsolvable: The function in the box could be 0 evereywhere, except for a single set of inputs, where it is 1. No strategy can guarantee that you find this set of inputs in finite time.
The situation might look better, if you can assume some sort of smoothness and/or monotony conditions.