How do humans optimize noisy multi-variable functions in experimental settings?
This is a bit of a tangential answer, but hopefully still useful.
When we give humans noisy data, we can basically think of them as some sort of Bayesian inference machines that try to figure out what the function that data came from looks like. The important thing we then need to know, is how strong of a bias (prior) humans have towards expecting certain relationships.
Unfortunately, it seems that humans are extremely biased towards positive linear relationships. I think this will make it very hard for them to optimize data presented as in your question, because they will constantly assume it comes from a straight line. This is really well captured by the following figure from Kalish et al. (2007):

The experiment that generated the above picture is rather different from the one you describe, but we can think of it is a very particular type of noise. A person at stage $n$ is given 25 $(x,y)$ pairs from the function at stage $n - 1$. The person is then tested by being given an x value and asked for a y, 25 times. The results of this are passed on to the person at trial $n + 1$ as the training data. Thus, we could think of the errors of person at stage n as noise/errors (although systematic errors) for the person at stage $n + 1$. As you can see, it doesn't take much of this noise to lose all structure of the function you started with and revert to the natural bias of a positive linear relationship. In fact, in condition 1 participants are already completely confused about the U-shaped function after strage $n = 1$ (so the first participant, with no error already has a hard time understanding the function from $(x,y)$ pairs).
References
Kalish, M. L., Griffiths, T. L., &amp; Lewandowsky, S. (2007). Iterated learning: Intergenerational knowledge transmission reveals inductive biases. Psychonomic Bulletin &amp; Review, 14(M), 288-294. [pdf]