How is the backward pass performed in MADDPG algorithm from MARL

I'm using the MADDPG algorithm from https://github.com/openai/maddpg/blob/master/maddpg/trainer/maddpg.py. I understood the forward pass for both the actor and critic networks. I'm not able to understand how the actor and critic networks are updates. Like at line 188 and 191 the authors compute the critic loss and actor loss. But can anyone explain how the critic and actor networks are updated. Also, as far as I understand, when the number of agents increases from 3 to 6 for a simple spread policy in MADDPG, the computation time for Q loss and P loss at lines 188 and 191 increase super-linearly. I'm assuming this might be because both the Q loss and P loss utilize the Q values and the dimension to calculate the Q values increases with the number of increasing linearly. It would be great if anyone can help me to understand this back propagation phase much better and why does the computation time grow super-linearly. I also put a time counter to track the computation time of Q loss and P loss for 60,000 episodes with simple spread policy (3 agents, 3 landmarks, 0 adversaries). Thanks for the help, in advance!

**Q loss**
3 agents 74.31 sec
6 agents 243.31 sec (3X)
**P loss**
3 agents 114.86 sec
6 agents 321.76 sec (3x)