We describe work to control graphics rendering under limited computational resources by taking a decision-theoretic perspective on perceptual costs and computational savings of approximations. The work extends earlier work on the control of rendering by introducing methods and models for computing the expected cost associated with degradations of scene components. The expected cost is computed by considering the perceptual cost of degradations and a probability distribution over the attentional focus of viewers. We review the critical literature describing findings on visual search and attention, discuss the implications of the findings, and introduce models of expected perceptual cost. Finally, we discuss policies that harness information about the expected cost of scene components.