Title: Greedy Information Maximization for Online Feature Selection. Abstract: Feature selection is commonly used to reduce feature acquisition costs, but the standard approach is to train models with static feature subsets. Here, we consider the online feature selection problem, where the model can adaptively query features based on the presently available information. Online feature selection has mainly been viewed as a reinforcement learning problem, but we propose a simpler approach of greedily selecting features that maximize mutual information with the response variable. This intuitive idea is difficult to implement without perfect knowledge of the joint data distribution, so we propose a deep learning approach that recovers the greedy procedure when perfectly optimized. We apply our approach to numerous datasets and observe better performance than both RL-based and offline feature selection methods