Due to QFT books, we measure pole mass(physical mass) in experiments. From the Lagrangian point of view, renormalized mass is a parameter(in MS bar or some similar renormalization scheme that has an explicit renormalization scale)
We fix renormalized parameters ( renormalized mass, renormalized couplings and ...) at specific energy scale by experiments.
But the problem is that how do we measure renormalized mass? beacuase in any expriment we measure pole mass which is scale independent
For other renormalized parameters, I have no problem.