Hello Rufos
The answer is no - rendering scenes with moving objects requires GI calculation on every frame, and 3-4 minutes per is a very acceptable render-time.
You can speed up calculations by optimizing your scene for faster rendering , sometimes it is even possible to divide your scene on static and dynamic part , like to following example:
Chaos: Industry-leading design and visualization software … and you can render static objects with fly-through approach, Chaos: Industry-leading design and visualization software and then render dynamic objects with moving-objects approach.