This problem is well known in optimization. The A/B testing approch, when use correctly, provides a local optimization method that will bring you closer to the local maxima (or minima by inverting the metric sign). Note however that it is not the most efficient.

To locate the global maxima, if you have no prior knowledge on the underlying function, you have to pick very different starting points and apply the local optimization algorithm. The starting points may be picked at random, or in a grid for complete scanning or preferably using some priori knowledge which we do have on web services efficiency.