  With the help of massive data and rich computational resources, deep
Q-learning has been widely used in operations research and management science
and has contributed to great success in numerous applications, including
recommender systems, supply chains, games, and robotic manipulation. However,
the success of deep Q-learning lacks solid theoretical verification and
interpretability. The aim of this paper is to theoretically verify the power of
depth in deep Q-learning. Within the framework of statistical learning theory,
we rigorously prove that deep Q-learning outperforms its traditional version by
demonstrating its good generalization error bound. Our results reveal that the
main reason for the success of deep Q-learning is the excellent performance of
deep neural networks (deep nets) in capturing the special properties of rewards
namely, spatial sparseness and piecewise constancy, rather than their large
capacities. In this paper, we make fundamental contributions to the field of
reinforcement learning by answering to the following three questions: Why does
deep Q-learning perform so well? When does deep Q-learning perform better than
traditional Q-learning? How many samples are required to achieve a specific
prediction accuracy for deep Q-learning? Our theoretical assertions are
verified by applying deep Q-learning in the well-known beer game in supply
chain management and a simulated recommender system.
