  Packet routing is one of the fundamental problems in computer networks in
which a router determines the next-hop of each packet in the queue to get it as
quickly as possible to its destination. Reinforcement learning (RL) has been
introduced to design autonomous packet routing policies with local information
of stochastic packet arrival and service. However, the curse of dimensionality
of RL prohibits the more comprehensive representation of dynamic network
states, thus limiting its potential benefit. In this paper, we propose a novel
packet routing framework based on \emph{multi-agent} deep reinforcement
learning (DRL) in which each router possess an \emph{independent} LSTM
recurrent neural network for training and decision making in a \emph{fully
distributed} environment. The LSTM recurrent neural network extracts routing
features from rich information regarding backlogged packets and past actions,
and effectively approximates the value function of Q-learning. We further allow
each route to communicate periodically with direct neighbors so that a broader
view of network state can be incorporated. Experimental results manifest that
our multi-agent DRL policy can strike the delicate balance between
congestion-aware and shortest routes, and significantly reduce the packet
delivery time in general network topologies compared with its counterparts.
