How well does gradient descent work on extremely noisy data?

I'm interested in using gradient descent to predict the probability that a website visitor will click on an ad, given a number of things we know about them (geographic location, browser, operating system, referrer, etc).

Typical click-rates are around 0.1%, and obviously there are a lot of factors that play a part in whether or not the user clicks that aren't represented in the input attributes. This means that from the learning algorithm's perspective the output data is extremely noisy.

How well does gradient descent work on this kind of problem where you're essentially trying to pick out comparatively subtle relationships between the input and output data amidst a lot of noise?

Would a data mining approach be more effective here?

edit: In response to some comments, yes - I would use a logistic regression of some form because the output must be a probability.

edit2: In response to those asking about my cost function - my ultimate goal is, given multiple ads to choose from to show to a user, pick the one they are most likely to click on.