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Information-seeking conversation systems are increasingly popular in real-world applications, especially for e-commerce companies. To retrieve appropriate responses for users, it is necessary to compute the matching degrees between candidate responses and users' queries with historical dialogue utterances. As the contexts are usually much longer than responses, it is thus necessary to expand the responses (usually short) with richer information. Recent studies on pseudo-relevance feedback (PRF) have demonstrated its effectiveness in query expansion for search engines, hence we consider expanding response using PRF information. However, existing PRF approaches are either based on heuristic rules or require heavy manual labeling, which are not suitable for solving our task. To alleviate this problem, we treat the PRF selection for response expansion as a learning task and propose a reinforced learning method that can be trained in an end-to-end manner without any human annotations. More specifically, we propose a reinforced selector to extract useful PRF terms to enhance response candidates and a BERT-based response ranker to rank the PRF-enhanced responses. The performance of the ranker serves as a reward to guide the selector to extract useful PRF terms, which boosts the overall task performance. Extensive experiments on both standard benchmarks and commercial datasets prove the superiority of our reinforced PRF term selector compared with other potential soft or hard selection methods. Both case studies and quantitative analysis show that our model is capable of selecting meaningful PRF terms to expand response candidates and also achieving the best results compared with all baselines on a variety of evaluation metrics. We have also deployed our method on online production in an e-commerce company, which shows a significant improvement over the existing online ranking system.