When finding the best angles for QAOA we optimize over $F_{p}(\beta , \gamma) = \langle \psi_p(\gamma,\beta)|C|\psi_p(\gamma,\beta)\rangle $.
In each optimization step we simulate the circuit $m$ times and then calculate the mean $\mu$ of the outcomes which is $F_{p}(\beta , \gamma) = \langle \psi_p(\gamma,\beta)|C|\psi_p(\gamma,\beta)\rangle $.
What would happen if we don't optimize over the mean but on the maximum of the results of the simulation
Wouldn't it be much more efficient as fewer shots are needed for each simulation?
Are there any papers or work about this?