  Transforming a causal system from a given initial state to a desired target
state is an important task permeating multiple fields including control theory,
biology, and materials science. In causal models, such transformations can be
achieved by performing a set of interventions. In this paper, we consider the
problem of identifying a shift intervention that matches the desired mean of a
system through active learning. We define the Markov equivalence class that is
identifiable from shift interventions and propose two active learning
strategies that are guaranteed to exactly match a desired mean. We then derive
a worst-case lower bound for the number of interventions required and show that
these strategies are optimal for certain classes of graphs. In particular, we
show that our strategies may require exponentially fewer interventions than the
previously considered approaches, which optimize for structure learning in the
underlying causal graph. In line with our theoretical results, we also
demonstrate experimentally that our proposed active learning strategies require
fewer interventions compared to several baselines.
