# Dueling DQN - Advantage Stream, why use average and not the tanh?

For Dueling DQN (page 5), why do authors use an average for Advantage stream, and don't simply "activate" the Advantage stream (with a $tanh$ for example)?

Would "activating" work in theory, and is it a similar idea to what the authors intended to achieve, or am I missing the point?

To remind, this is the equation, which Produces a Q-value for the taken action $a$ by combining the Value stream with the Advantage stream:

$$Q(s,a; \theta, \alpha, \beta) = V(s; \theta, \beta) + \biggl( A(s, a; \theta, \alpha) - \frac{1}{N}\sum_{a'}^{N}A(s, a'; \theta, \alpha) \biggr)$$

where

• $s$ is the current state we are in
• $a$ is the action we've decided to take
• $a'$ is one of any action we could have taken (including the action we've taken)
• $\theta$ are parameters (weights) of the network before the "splitting" into two separate streams
• $\alpha$ are the parameters of Advantage stream
• $\beta$ are the parameters of the Value stream