A fundamental challenge to modern science and engineering is that of rapidly and accurately sensing the environment. Harmful algae blooms impair access to drinking water, wildfires present a persistent threat to safety in the western United States, and traffic and industry-related air pollutants pose a risk to growing urban populations. To combat these issues, researchers are turning increasingly to mobile sampling devices to provide safe, persistent estimation of environmental phenomena. However, given the vast spatial regions these devices are tasked with covering, a key open problem is that of designing sampling strategies to provide the highest quality of information given the available resources. This project aims to enable mobile sampling devices to perform efficient, autonomous monitoring of such phenomena, thereby permitting scientists and other concerned actors to make informed, data-driven decisions. The project also facilitates undergraduate involvement through the deployment of the developed algorithms on an unmanned aerial system, as well as workshops to engage underrepresented community college students in the project goals.<br/><br/>A key task in environmental sensing is that of determining where a phenomenon lies above a certain threshold (for example, regions where the pollution level is above a safe limit), a problem known as level-set estimation (LSE). Existing LSE algorithms fall short by either (1) failing to incorporate sampling costs associated with mobile sensors, (2) lacking theoretical guarantees, or (3) relying on strong modeling assumptions. The technical aim of this project is the development of practical adaptive sampling algorithms for LSE with well-understood theoretical properties. The first thrust of the project will consider the problem of estimating the change point of a step function in one dimension, drawing on connections between active learning and robotic path planning to develop and analyze algorithms capable of incorporating previously-ignored costs and handling noisy measurements. The second thrust will consider the two-dimensional LSE problem directly via a graph-based approach. By combining recent techniques from graph-based active learning with Markov decision processes and reinforcement learning, realistic sampling costs based on the distance traveled, the number of measurements taken, and the need to return to a base station for battery recharging will be incorporated.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.