Prediction in a new domain without any training sample, called zero-shot domain adaptation (ZSDA), is an important task in domain adaptation. While prediction in a new domain has gained much attention in recent years, in this paper, we investigate another potential of ZSDA. Specifically, instead of predicting responses in a new domain, we find a description of a new domain given a prediction. The task is regarded as predictive optimization, but existing predictive optimization methods have not been extended to handling multiple domains. We propose a simple framework for predictive optimization with ZSDA and analyze the condition in which the optimization problem becomes convex optimization. We also discuss how to handle the interaction of characteristics of a domain in predictive optimization. Through numerical experiments, we demonstrate the potential usefulness of our proposed framework.