When is it necessary to explicitly define both the state and observation space in a custom environment?

Question

I'm fairly new to reinforcement learning concepts, and I'm trying to implement a simple custom environment. In my custom environment, I have a scenario where I have multiple continuous state spaces, for example, length(l), and breadth(b), from which I calculate say, area(a) = l*b. I calculate the reward based on the area. Here I check if the area lies between the range I'm expecting it to and reward it accordingly.

Since my reward is based on the area which is f(l, b) = l*b, should I declare the observation space as the range of values my area can attain? Or should I declare my observation space as the values the length(l) and breadth(b) can attain? Or is my understanding wrong?

Area(a) = f(l, b) = l*b
Reward = +1 (if 15 < a < 20)
         -.1 (otherwise)

Answer 1

The observation space and the state space are not the same in general. There exist problems where the state space cannot be fully observed, which goes by the name Partially Observable Reinforcement Learning (or some variation of it). This is relevant in environments with imperfect information. To me, it does not look like you are dealing with partial observation here, therefore state and observation space are identical.

Let's say e.g. for a poker game the state and the observation space are different, because the state space is the space of all the cards and money of all players (+ the order of play) and the community cards, while the observation space from one agent is only his own cards + community cards and the money. The observation space does not include the cards of the opposite players.