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Recently, increasing attention has been paid to heterogeneous graph representation learning (HGRL), which aims to embed rich structural and semantic information in heterogeneous information networks (HINs) into low-dimensional node representations. To date, most HGRL models rely on hand-crafted meta-paths. However, the dependency on manually-defined meta-paths requires domain knowledge, which is difficult to obtain for complex HINs. More importantly, the pre-defined or generated meta-paths of all existing HGRL methods attached to each node type or node pair cannot be personalised to each individual node. To fully unleash the power of HGRL, we present a novel framework, Personalised Meta-path based Heterogeneous Graph Neural Networks (PM-HGNN), to jointly generate meta-paths that are personalised for each individual node in a HIN and learn node representations for the target downstream task like node classification. Precisely, PM-HGNN treats the meta-path generation as a Markov Decision Process and utilises a policy network to adaptively generate a meta-path for each individual node and simultaneously learn effective node representations. The policy network is trained with deep reinforcement learning by exploiting the performance improvement on a downstream task. We further propose an extension, PM-HGNN++, to better encode relational structure and accelerate the training during the meta-path generation. Experimental results reveal that both PM-HGNN and PM-HGNN++ can significantly and consistently outperform 16 competing baselines and state-of-the-art methods in various settings of node classification. Qualitative analysis also shows that PM-HGNN++ can identify meaningful meta-paths overlooked by human knowledge.