In reinforcement learning, there are states, actions, initial states, terminal states, a progress function and a reward function. Is there a theoretical framework or setting where states and actions are from the same domain?

So the goal would be to learn a policy to manipulate an input stream in a way that optimizes a reward function. Input would be a state vector and output (i.e. action) would be another vector of the same domain.

  • $\begingroup$ A policy in reinforcement learning is a function mapping states to each other. It's a sort of instruction manual for what to do from each state, rather than a vector. It sounds like you're trying to choose the input that optimizes an objective function, is that right? $\endgroup$ – Sean Easter Feb 19 '16 at 21:45

This is the case when for example you have $\mathcal{S} \triangleq \mathbb{R}^d, \mathcal{A} \triangleq \mathbb{R}^d$ like 2d navigation with $d = 2$ (states are locations, actions are vectors indicating direction). Doing RL in that case does not change and there is not special theory either.

  • $\begingroup$ Well, I guess the domain of actions is restricted to a certain maximum vector length and the state domain is not. What I was thinking about is the objective of "(slightly) manipulate the input in a way that maximizes the reward". $\endgroup$ – danijar Jan 29 '16 at 14:33

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