I am confused about the definition of the optimal value ($V^*$) and optimal action-value (Q*) in reinforcement learning, so I need some clarification, because some blogs I read on Medium and GitHub are inconsistent with the literature.
Originally, I thought the optimal action value, $Q^*$, represents you performing the action that maximizes your current reward, and then acting optimally thereafter.
And the optimal value, $V^*$, being the average $Q$ values in that state. Meaning that if you're in this state, the average "goodness" is this.
For example: If I am in a toy store and I can buy a pencil, yo-yo, or Lego.
Q(toy store, pencil) = -10 Q(toy store, yo-yo) = 5 Q(toy store, Lego) = 50
And therefore my $Q^* = 50$
But my $V^*$ in this case is:
V* = -10 + 5 + 50 / 3 = 15
Representing no matter what action I take, the average future projected reward is $15$.
And for the advantage of learning, my baseline would be $15$. So anything less than $0$ is worse than average and anything above $0$ is better than average.
However, now I am reading about how $V^*$ actually assumes the optimal action in a given state, meaning $V^*$ would be 50 in the above case.
I am wondering which definition is correct.