Blockchain is an essentially distributed database recording all transactions or digital events among participating parties. Each transaction in the records is approved and verified by consensus of the participants in the system that requires solving a hard mathematical puzzle, which is known as proof-of-work. To make the approved records immutable, the mathematical puzzle is not trivial to solve and therefore consumes substantial computing resources. However, it is energy-wasteful to have many computational nodes installed in the blockchain competing to approve the records by just solving a meaningless puzzle. Here, we pose proof-of-work as a reinforcement-learning problem by modeling the blockchain growing as a Markov decision process, in which a learning agent makes an optimal decision over the environment's state, whereas a new block is added and verified. Specifically, we design the block verification and consensus mechanism as a deep reinforcement-learning iteration process. As a result, our method utilizes the determination of state transition and the randomness of action selection of a Markov decision process, as well as the computational complexity of a deep neural network, collectively to make the blocks not easy to recompute and to preserve the order of transactions, while the blockchain nodes are exploited to train the same deep neural network with different data samples (state-action pairs) in parallel, allowing the model to experience multiple episodes across computing nodes but at one time. Our method is used to design the next generation of public blockchain networks, which has the potential not only to spare computational resources for industrial applications but also to encourage data sharing and AI model design for common problems.