We develop an approach to policy selection in active inference that allows us to efficiently search large policy spaces by mapping each policy to its embedding in a vector space. We sample the expected free energy of representative points in the space, then perform a more thorough policy search around the most promising point in this initial sample. We consider various approaches to creating the policy embedding space, and propose using k-means clustering to select representative points. We apply our technique to a goal-oriented graph-traversal problem, for which naive policy selection is intractable for even moderately large graphs.