Do you have a specific PBT implementation you are considering ?

Yes. Ray has a nice implementation of that and of many other things (It also supports Optuna & BOHB internally). This could relate to a https://github.com/allegroai/trains/issues/227#issuecomment-716513710 I opened in the GIT.

TPE and HBOB are competitive to PBT in terms of performance

Yes, and I believe ASHA is also, but I wanted to compare PBT.

Thanks anyway.