It can largely benefit the reinforcement learning process of each agent if multiple agents perform their separate reinforcement learning tasks cooperatively. These tasks can be not exactly the same but still benefit from the communication behaviour between agents due to task similarities. In fact, this learning scenario is not well understood yet and not well formulated. As the first effort, we provide a detailed discussion of this scenario, and propose group-agent reinforcement learning as a formulation of the reinforcement learning problem under this scenario and a third type of reinforcement learning problem with respect to single-agent and multi-agent reinforcement learning. We propose that it can be solved with the help of modern deep reinforcement learning techniques and provide a distributed deep reinforcement learning algorithm called DDA3C (Decentralised Distributed Asynchronous Advantage Actor-Critic) that is the first framework designed for group-agent reinforcement learning. We show through experiments in the CartPole-v0 game environment that DDA3C achieved desirable performance with very stable training and has good scalability.