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From observational data alone, a causal DAG is only identifiable up to Markovequivalence. Interventional data generally improves identifiability; however,the gain of an intervention strongly depends on the intervention target, thatis, the intervened variables. We present active learning (that is, optimalexperimental design) strategies calculating optimal interventions for twodifferent learning goals. The first one is a greedy approach usingsingle-vertex interventions that maximizes the number of edges that can beoriented after each intervention. The second one yields in polynomial time aminimum set of targets of arbitrary size that guarantees full identifiability.This second approach proves a conjecture of Eberhardt (2008) indicating thenumber of unbounded intervention targets which is sufficient and in the worstcase necessary for full identifiability. In a simulation study, we compare ourtwo active learning approaches to random interventions and an existingapproach, and analyze the influence of estimation errors on the overallperformance of active learning.

Two Optimal Strategies for Active Learning of Causal Models from Interventional Data