I'm currently working on a multi-agent reinforcement learning. The setting is a cooperative multi-agent system with a stationary assumption on the opponent policy. Suppose I have the model of the opponent policy $\rho(\cdot|s_t)$, where $s_t$ denotes the environment state at time $t$. I'm currently wondering how to actually make use of it to design our controllable agent policy $\pi(\cdot|s_t)$?

Intuitively, I think the form of the policy should be like $\pi(\cdot|s_t,\rho(\cdot|s_t))$. Yet, I don't have any idea to parameterize the expression, i.e. make it as a functional form $\pi(\cdot|s_t,\rho(\cdot|s_t)) = f(s_t,\rho(\cdot|s_t))$. Does anyone have some clue with a sound/best practice parameterization? Any thought would be appreciated.


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