complexity theory – BPP and BQP: Optimization Versions?

For optimization problems, I found complexity classes analog to some classes for decision problems, e.g. PO and NPO, mirroring P and NP for decision problems in the sense that optimization problems in PO can be solved in polynomial time and verified in polynomial time, respectively.

Are there similar class definitions mirroring BPP and BQP, i.e. classes of optimization problems that could be solved with a probabilistic algorithm or on a quantum computer efficiently?