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?

Is there a practical strategy that can learn to price a product optimally? Right now I have the following 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?