# How can I convert the problem formulation to multi-agent reinforcement learning?

I'm trying to minimize the power consumption in wireless networks and I have some constraints such as that the SINR should not pass the threshold and the power should be between the 0 and maximum power and other constraints. I'm trying to formulate my problem to be similar to equation 8 in this paper 'Distributed Optimization for Coordinated Beamforming in Multicell Multigroup Multicast Systems: Power Minimization and SINR Balancing.

$$$$\min \sum_{i=1}^{N}P(i)$$$$ subject to

$$$$\sum_{i=1}^{N} Status_i\leq N \nonumber,$$$$ $$$$Status_i= \begin{cases} 1, & \text{if node i is active } \\ 0, & \text{otherwise} \end{cases} \nonumber,$$$$ $$$$1-P(C_{i,k}>T_F ) \leq p_{cov} \nonumber.$$$$ $$$$0\le P(i) \le P_{max}$$$$ $$$$\gamma_{k_i,k_j} \le \theta$$$$

where $$N$$ represents the number of the nodes while $$Status_i$$ shows if the node is active or not. $$T_F$$ and $$\theta$$ represent the SINR $$\gamma_{k_i,k_j}$$ threshold for the node.

The coverage probability $$p_{cov} = P[\gamma_{k_i,k_j}> \theta ]$$ .

I need to convert this problem to be represented as multi-agent reinforcement learning. The problem is that I don't know how to define the state, the action, and the reward. Can someone help me?

• Figuring out how to model your system as an RL task will take domain expertise. Could you edit your question to be much more descriptive? References always help. Be sure to define your terms. – Philip Raeisghasem Apr 6 at 9:56
• @PhilipRaeisghasem I'm trying to build my own problem which is similar to the equation 8 in this paper 'Distributed Optimization for Coordinated Beamforming in Multicell Multigroup Multicast Systems: Power Minimization and SINR Balancing' – i_th Apr 6 at 10:22
• I recommend posting the relevant parts here – hisairnessag3 Apr 6 at 23:42
• @hisairnessag3 I already share my problem formulation. – i_th Apr 7 at 5:42
• @i_th I mean the equation. As well as the relevant literature. Not many contributors are going to want to log into the IEEE accts, find the parts you mention and then decipher it from there. – hisairnessag3 Apr 7 at 5:48