I know every engineering works is based on compromises, and rocket design is no exception. A rocket should go as quickly as possible to high altitude to avoid flying for a long time and at high speed into the atmosphere.
Moreover, the rocket may accelerate more and more as it is lighter while burning fuel and the engines remain the same (almost the same thrust).
Climbing faster may increase max Q (high speed at lower altitude).
Accelerating too quickly may exceed payload acceleration tolerances.
Accelerating quickly requires powerful engines (and perhaps few fuel or smaller tanks to reduce weight).
Not knowing all the constraints and parameter to optimize for rocket launch, I wonder if there is an optimal acceleration profile for launcher take off. As it seems broad, the question is restricted to the first minutes of flights (more or less from take off to 150 km high) and to flights putting payload into LEO.