In radiation therapy treatment-plan optimization, selecting a set of clinical objectives that are tractable and parsimonious yet effective is a challenging task. In clinical practice, this is typically done by trial and error based on the treatment planner's subjective assessment, which often makes the planning process inefficient and inconsistent. We develop the objective selection problem that infers a sparse set of objectives for prostate cancer treatment planning based on historical treatment data. We formulate the problem as a non-convex bilevel mixed-integer program using inverse optimization and highlight its connection with feature selection to propose multiple solution approaches, including greedy heuristics, regularized problems, as well as application-specific methods that utilize anatomical information of the patients. Our results show that the proposed heuristics find objectives that are near optimal. Via curve analysis on dose-volume histograms, we show that the learned objectives closely represent latent clinical preferences.