Recent years have seen proposals for exciting new computational display technologies that are compressive in the sense that they generate high resolution images or light fields with relatively few display parameters. Image synthesis for these types of displays involves two major tasks: sampling and rendering high-dimensional target imagery, such as light fields or time-varying light fields, as well as optimizing the display parameters to provide a good approximation of the target content. In this paper, we introduce an adaptive optimization framework for compressive displays that generates high quality images and light fields using only a fraction of the total plenoptic samples. We demonstrate the framework for a large set of display technologies, including several types of auto-stereoscopic displays, high dynamic range displays, and high-resolution displays. We achieve significant performance gains, and in some cases are able to process data that would be infeasible with existing methods.