Is there a practical strategy that can learn to price a product optimally? Right now I have the following, somewhat arbitrary hill-climbing algorithm:

- Run an experiment at starting price `P` and gather 500 data points (e.x. 20 buy and 480 not buy). 
- Run a t-test on what confidence level `P` yields higher revenue per visitor than `P * 1.1` and `P * 0.9`. Then do a 3-way weighted coin-flip and the winner gets to run the next experiment.

There's many problems with this approach. For example, if price is at optimal, it can't price a product at a more optimal pricing e.x. `P * 1.03`. Another is that if at some price point `P = K` we happen to get really unlucky and get 1 buy of 500 data points, the algorithm won't converge fast.

The problem gets easy if we take lots of data points but that would reduce long term revenue. Is there a fast algorithm that can converge to the optimal price and then not do anymore exploration?