It really depends on what you're using to create the boost and where it is on its efficiency map for the amount of airflow needed to generate the boost you are running. Remember that boost just is positive pressure in the intake, it can be generated by putting cramming more air in, or heating the air up.

I.E. You can take a 6-71 and overdrive it until it makes 20 PSI on a 440, but its outside and above the efficiency range of the compressor, so most of the boost is a function of heat and NOT cramming air into the engine.

You might put an 8-71 or 10-71 and it will make more power at the same 20 PSI, and it might make more power at 12 PSI than the 6-71 did at 20 PSI.

As dogdays said above, in my opinion, it is not X HP for each PSI, it is related to the HP the engine makes NA. In theory 14.7 PSI would double your horsepower at sealevel, but it doesn't work that way for a variety of reasons. It MIGHT in a certain application. The tune up changes more as you increase boost, which limits the effect. But you might get 2X hp @ 14.7 PSI running a compressor well within its efficiency map on 118 octane, maybe with alcohol injection too. The efficiency of the combustion chamber would play a role here too.

I usually use this to get an idea and its always pretty close for me, but its HIGHLY SUBJECTIVE: Theoretical NA HP + (Theoretical NA HP * ((Boost/14.7)* estimated efficiency)) = HP

The Estimated efficiency here is highly subjective. On supercharged applications running PUMP GAS usually an efficiency of .6-.65 produces an accurate output if the supercharger is sized correctly for the application. On turbocharged and intercooled applications if the turbo is being pushed towards the upper end of the efficiency range around .7-.75 will work well. If its at the lower end or sweet spot around .8-.85 will work well. Again, this is on pump gas.

But if you got a huge turbo capable of generating 40 PSI efficiently on an engine and you only run 10 PSI you're likely going to be at or slightly over 100% efficiency. So really, to answer your question, no there is not. But the formula above usually works pretty well for me. Its just all subjective to what efficiency you use, but I'm pretty good at guesstimating that. Its all just a guess though.

Also, the fuel makes a BIG effect on the outcome. The bigger the boost the more the fuel can affect it.