Parameter Sharing in Coagent Networks

In this paper, we aim to prove the theorem that generalizes the Coagent Network Policy Gradient Theorem (Kostas et. al., 2019) to the context where parameters are shared among the function approximators involved. This provides the theoretical foundation to use any pattern of parameter sharing and leverage the freedom in the graph structure of the network to possibility exploit relational bias in a given task. As another application, we will apply our result to give a more intuitive proof for the Hierarchical Option Critic Policy Gradient Theorem, first shown in (Riemer et. al., 2019).