# In a DDQN architecture, why is the value of a state assumed to be the average of the Q values of the actions?

In a Dueling DQN agent (Wang et al.), the Q function is decomposed as

$$Q(s, a)=V(s) + A(s, a) - \frac{1}{|A|}\sum_{a'\in \mathcal{A}}A(s, a')$$

representing the value of the state, plus the advantage of the action, minus the average advantage of all actions available in that state.

However, this formulation means that the value of the given state is skewed, even after subtracting out the mean advantage of all actions available. Why isn't it set up so that the advantage of the best action is 0 (with the other actions' advantages being negative), thus leading to a more accurate $$V(s)$$?

Furthermore, the authors attempt a softmax version, but they find it doesn't perform that differently than the average-advantage version. I couldn't find any additional experiments using this, but it may be worth trying if it is absolutely necessary to obtain an accurate $$V(s)$$.