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Unstructured Persona-oriented Dialogue Systems (UPDS) has been demonstrated effective in generating persona consistent responses by utilizing predefined natural language user persona descriptions (e.g., "I am a vegan"). However, the predefined user persona descriptions are usually short and limited to only a few descriptive words, which makes it hard to correlate them with the dialogues. As a result, existing methods either fail to use the persona description or use them improperly when generating persona consistent responses. To address this, we propose a neural topical expansion framework, namely Persona Exploration and Exploitation (PEE), which is able to extend the predefined user persona description with semantically correlated content before utilizing them to generate dialogue responses. PEE consists of two main modules: persona exploration and persona exploitation. The former learns to extend the predefined user persona description by mining and correlating with existing dialogue corpus using a variational auto-encoder (VAE) based topic model. The latter learns to generate persona consistent responses by utilizing the predefined and extended user persona description. In order to make persona exploitation learn to utilize user persona description more properly, we also introduce two persona-oriented loss functions: Persona-oriented Matching (P-Match) loss and Persona-oriented Bag-of-Words (P-BoWs) loss which respectively supervise persona selection in encoder and decoder. Experimental results show that our approach outperforms state-of-the-art baselines, in terms of both automatic and human evaluations.