The paper addresses the fundamental task of semantic image analysis by exploiting structural information (spatial relationships between image regions). We propose to combine a deep neural network (CNN) with graph matching where graphs encode efficiently structural information related to regions segmented by the CNN. Our novel approach solves the quadratic assignment problem (QAP) sequentially for matching graphs. The optimal sequence for graph matching is conveniently defined using reinforcement-learning (RL) based on the region membership probabilities produced by the CNN and their structural relationships. Our RL-based strategy for solving QAP sequentially allows us to significantly reduce the combinatorial complexity for graph matching. Preliminary experiments are performed on both a synthetic dataset and a public dataset dedicated to the semantic segmentation of face images. Results show that the proposed RL-based ordering significantly outperforms random ordering and that our strategy is about 386 times faster than a global QAP-based approach while preserving similar segmentation accuracy.