The Transformer architecture has achieved remarkable success in a number of domains including natural language processing and computer vision. However, when it comes to graph-structured data, transformers have not achieved competitive performance, especially on large graphs. In this paper, we identify the main deficiencies of current graph transformers: (1) Existing node sampling strategies in Graph Transformers are agnostic to the graph characteristics and the training process. (2) Most sampling strategies only focus on local neighbors and neglect the long-range dependencies in the graph. We conduct experimental investigations on synthetic datasets to show that existing sampling strategies are sub-optimal. To tackle the aforementioned problems, we formulate the optimization strategies of node sampling in Graph Transformer as an adversary bandit problem, where the rewards are related to the attention weights and can vary in the training procedure. Meanwhile, we propose a hierarchical attention scheme with graph coarsening to capture the long-range interactions while reducing computational complexity. Finally, we conduct extensive experiments on real-world datasets to demonstrate the superiority of our method over existing graph transformers and popular GNNs.