The proliferation of modern smartphones has given rise to Public Sensing, a new paradigm for data acquisition systems utilizing smartphones of mobile participants. In this paper, we present DrOPS, a system for improving the efficiency of data acquisition in Public Sensing systems. DrOPS utilizes a model-driven approach, where the number of required readings from mobile smartphones is reduced by inferring readings from the model. Furthermore, the model can be used to infer readings for positions where no sensor is available. The model is directly constructed from the observed phenomenon in an online fashion. Using such models together with a client-specified quality bound, we can significantly reduce the effort for data acquisition while still reporting data of required quality to the client. To this effect, we develop a set of online learning and control algorithms to create and validate the model of the observed phenomenon and present a sensing task execution system utilizing our algorithms in this paper. Our evaluations show that we obtain models in a matter of just hours or even minutes. Using the model-driven approach for optimizing the data acquisition, we can save up to 80% of energy for communication and provide inferred temperature readings for uncovered positions matching an error-bound of 1°C up to 100% of the time.