Relevant and high-quality data are critical to successful development of machine learning applications. For machine learning applications on dynamic systems equipped with a large number of sensors, such as connected vehicles and robots, how to find relevant and high-quality data features in an efficient way is a challenging problem. In this work, we address the problem of feature selection in constrained continuous data acquisition. We propose a feedback-based dynamic feature selection algorithm that efficiently decides on the feature set for data collection from a dynamic system in a step-wise manner. We formulate the sequential feature selection procedure as a Markov Decision Process. The machine learning model performance feedback with an exploration component is used as the reward function in an $epsilon$-greedy action selection. Our evaluation shows that the proposed feedback-based feature selection algorithm has superior performance over constrained baseline methods and matching performance with unconstrained baseline methods.