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Waterfall Recommender System (RS), a popular form of RS in mobile applications, is a stream of recommended items consisting of successive pages that can be browsed by scrolling. In waterfall RS, when a user finishes browsing a page, the edge (e.g., mobile phones) would send a request to the cloud server to get a new page of recommendations, known as the paging request mechanism. RSs typically put a large number of items into one page to reduce excessive resource consumption from numerous paging requests, which, however, would diminish the RSs' ability to timely renew the recommendations according to users' real-time interest and lead to a poor user experience. Intuitively, inserting additional requests inside pages to update the recommendations with a higher frequency can alleviate the problem. However, previous attempts, including only non-adaptive strategies (e.g., insert requests uniformly), would eventually lead to resource overconsumption. To this end, we envision a new learning task of edge intelligence named Intelligent Request Strategy Design (IRSD). It aims to improve the effectiveness of waterfall RSs by determining the appropriate occasions of request insertion based on users' real-time intention. Moreover, we propose a new paradigm of adaptive request insertion strategy named Uplift-based On-edge Smart Request Framework (AdaRequest). AdaRequest 1) captures the dynamic change of users' intentions by matching their real-time behaviors with their historical interests based on attention-based neural networks. 2) estimates the counterfactual uplift of user purchase brought by an inserted request based on causal inference. 3) determines the final request insertion strategy by maximizing the utility function under online resource constraints. We conduct extensive experiments on both offline dataset and online A/B test to verify the effectiveness of AdaRequest.