  Network slicing promises to provision diversified services with distinct
requirements in one infrastructure. Deep reinforcement learning (e.g., deep
$\mathcal{Q}$-learning, DQL) is assumed to be an appropriate algorithm to solve
the demand-aware inter-slice resource management issue in network slicing by
regarding the varying demands and the allocated bandwidth as the environment
state and the action, respectively. However, allocating bandwidth in a finer
resolution usually implies larger action space, and unfortunately DQL fails to
quickly converge in this case. In this paper, we introduce discrete normalized
advantage functions (DNAF) into DQL, by separating the $\mathcal{Q}$-value
function as a state-value function term and an advantage term and exploiting a
deterministic policy gradient descent (DPGD) algorithm to avoid the unnecessary
calculation of $\mathcal{Q}$-value for every state-action pair. Furthermore, as
DPGD only works in continuous action space, we embed a k-nearest neighbor
algorithm into DQL to quickly find a valid action in the discrete space nearest
to the DPGD output. Finally, we verify the faster convergence of the DNAF-based
DQL through extensive simulations.
