There is a question already about applying RL to "large scale problems", where large scale refers to the problem of a relatively small number of actions (that could be from a continous space) resulting in a very large number of states.
A good exapmle of this kind of large-scale probems is modeling a motion of a boat as a point on a plane, with an action being a displacement vector $\mathbf{\delta}_b = (\delta_x, \delta_y)$ and there are infinitely many states, because the next state is given by the next position of the boat, in a circle surrounding the boat $\mathcal{B}(\mathbf{x}_b, \mathbf{\delta}_{b,max})$, where $\mathbf{x_b}$ is the boat's current position, and $\mathbf{\delta}_{b,max}$ the maximal possible displacement. So here, the displacement as an action (move the boat) is from an infinite space because it is a 2D vector ($\delta_b \in \subset \mathbb{R}^2$) and so is the state space $\mathcal{B}$. Still, I just have two actions to apply to the boat in the end: move in x-directions this much, and in y-direction that much.
What I mean, is something even larger. Considering the example of a boat, is it possible to apply reinforcement learning on a system that has 100 000 of such boats, and what would be the methods to look into to accomplish this. I do not mean to have 100 000 agents. The agent in this scenario is observing 100 000 boats, they are its environment, and let's say the agent is distributing them in a current on the sea in such a way that they have the least amount of resistance in the water (the wake of one ship influences the resistance of its downstream neighbors).
From this answer and from what I have read so far, I believe an approximation will be necessary for the displacements in $2D$ space $\mathbf{\delta}(x,y)$ as well as for the states and rewards, because there are so many of them. However, before digging into this, I would like to know if there are some references out there where something like this has already been tried, or if this is simply something where RL cannot be applied.
