Hi @YL0910,
I you are looking to read more about the biological plausibility of the PES learning algorithm, I’d advise you check out @tbekolay’s Master’s thesis, and in particular, Chapter 4, where he describes the PES rule. Note that it wasn’t called the PES rule in the thesis, but the formulation is there. The name “prescribed error sensitivity” (PES) was coined after his thesis was published.
I also found a discussion here that might be relevant.