I know Deep Q network as a $S\times A$ DNN which maps the $S$ dimensional statespace to q-values of $A$ distinct actions.
In my problem, the action space is still discrete, and finite, but depending on some parameters (e.g. number of users in a system) can grow exponentially large. More concretely, if I have $n$ users, then there are about $3^n$ actions. Clearly, the vanilla DQN is infeasible for this problem.
So I wonder if there are any reference algorithms (best if they come with mature library supports for production code) catering to the scenarios where it is infeasible to calculate individual Q values for each action.