I'll have to see if I can find references to an older effort on previous learning algorithm optimizations with FPGAs in the loop - it must be 20+ years old by now. The algorithm did indeed optimize the toy problems that it was setup to optimize, but it exploited non-digital, analog electronic characteristics of the individual FPGA to do it, so the solutions were not portable to any other FPGA - even of the same model.

Edit: There it is, Adrian Thompson evolution of tone generators, 1997.

https://en.wikipedia.org/wiki/Evolvable_hardware