# In reinforcement learning, why are policies defined as functions of states and not observations?

I am new to RL and I am following Sutton & Barto's book.

My doubt is, when we talk about the policy of our agent, we say it is the probability of taking some action $$a$$ given the state $$s$$. However, I think that the policy should be defined in terms of observations and not states because I think it is not always possible for an agent to fully capture the state due to various reasons, maybe lack of sensors or lack of memory.

So, why are policies defined as functions of states and not observations?

• From what I remember, RL can handle POMDP. Sep 19 '21 at 4:47
• oh, I'll read about it, because I think one of the reason they defined it that way can be that, they mentioned the environment to be fully observable. But then how my agent is going to make actions? if i dont know what state I am in. It is all very confusing in my head @FourierFlux Sep 19 '21 at 5:10
• From what I remember something in Sutton's book says function based approximations can work on POMDP, but discrete state cannot. I would need to look it up though to be sure. Sep 19 '21 at 5:19
• To be honest though it shouldn't work intuitively speaking, since an RL problem should ultimately be a MDP and there cannot be hidden states which have memory so I do not know. Sep 19 '21 at 5:22
• @FourierFlux: I think you have remembered correctly. The key is that there are different degrees and types of missing knowledge that can impact an agent learning to act in an MDP. I think a good answer will try to cover that, as well as how observatons and state can interact. Sep 19 '21 at 8:58