Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for determining controls to be applied to a population of devices. In one aspect, a method comprises: determining a plurality of simulated load curves, wherein each simulated load curve simulates load generated by a respective device from a population of devices based on application of a respective control from a set of controls; adjusting values of a plurality of weights during a plurality of optimization iterations using an optimization technique to optimize a loss function, wherein each weight corresponds to a respective simulated load curve, wherein the loss function measures: a sparsity of the values of the plurality of weights, and an error between: (i) an aggregate load curve that is defined by combining the simulated load curves in accordance with the values of the plurality of weights, and (ii) a target load curve.