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Multi-stage cascade architecture exists widely in many industrial systems such as recommender systems and online advertising, which often consists of sequential modules including matching, pre-ranking, ranking, etc. For a long time, it is believed pre-ranking is just a simplified version of the ranking module, considering the larger size of the candidate set to be ranked. Thus, efforts are made mostly on simplifying ranking model to handle the explosion of computing power for online inference. In this paper, we rethink the challenge of the pre-ranking system from an algorithm-system co-design view. Instead of saving computing power with restriction of model architecture which causes loss of model performance, here we design a new pre-ranking system by joint optimization of both the pre-ranking model and the computing power it costs. We name it COLD (Computing power cost-aware Online and Lightweight Deep pre-ranking system). COLD beats SOTA in three folds: (i) an arbitrary deep model with cross features can be applied in COLD under a constraint of controllable computing power cost. (ii) computing power cost is explicitly reduced by applying optimization tricks for inference acceleration. This further brings space for COLD to apply more complex deep models to reach better performance. (iii) COLD model works in an online learning and severing manner, bringing it excellent ability to handle the challenge of the data distribution shift. Meanwhile, the fully online pre-ranking system of COLD provides us with a flexible infrastructure that supports efficient new model developing and online A/B testing.Since 2019, COLD has been deployed in almost all products involving the pre-ranking module in the display advertising system in Alibaba, bringing significant improvements.