Abstract: In-context learning is a new learning paradigm where a language model conditions on a few input-output pairs (demonstrations) and a test input, and directly outputs the prediction. It has been shown sensitive to the provided demonstrations and thus promotes the research of demonstration retrieval: given a test input, relevant examples are retrieved from the training set to serve as informative demonstrations for in-context learning. While previous works train task-specific retrievers for several tasks separately, these methods are hard to transfer and scale on various tasks, and separately trained retrievers will cause a lot of parameter storage and deployment cost. In this paper, we propose Unified Demonstration Retriever (UDR), a single model to retrieve demonstrations for a wide range of tasks. To train UDR, we cast various tasks' training signals into a unified list-wise ranking formulation by language model's feedback. Then we propose a multi-task list-wise ranking training framework with an iterative mining strategy to find high-quality candidates, which can help UDR fully incorporate various tasks' signals. Experiments on 30+ tasks across 13 task families and multiple data domains show that UDR significantly outperforms baselines. Further analyses show the effectiveness of each proposed component and UDR's strong ability in various scenarios including different LMs (1.3B ~ 175B), unseen datasets, varying demonstration quantities, etc. We will release the code and model checkpoint after review.