This improvement to DQN was proposed in 2015, in the paper called Dueling Network Architectures for Deep Reinforcement Learning ([8] Wang et al., 2015). The core observation of this paper lies in the fact that the Q-values Q(s, a) our network is trying to approximate can be divided into quantities: the value of the state V(s) and the advantage of actions in this state A(s, a). We've seen quantity V(s) before, as it was the core of the value iteration method from Chapter 5, Tabular Learning and the Bellman Equation. It just equals to the discounted expected reward achievable from this state. The advantage A(s, a) is supposed to bridge the gap from A(s) to Q(s, a), as, by definition: Q(s, a) = V(s) + A(s, a). In other words, the advantage A(s, a) is just the delta, saying how much extra reward some particular action from the state brings us. Advantage could be positive or negative and, in general, can have any magnitude. For example, at some tipping point, the choice of one...