  We analyze the sample complexity of learning from multiple experiments where
the experimenter has a total budget for obtaining samples. In this problem, the
learner should choose a hypothesis that performs well with respect to multiple
experiments, and their related data distributions. Each collected sample is
associated with a cost which depends on the particular experiments. In our
setup, a learner performs $m$ experiments, while incurring a total cost $C$. We
first show that learning from multiple experiments allows to improve
identifiability. Additionally, by using a Rademacher complexity approach, we
show that the gap between the training and generalization error is
$O(C^{-1/2})$. We also provide some examples for linear prediction, two-layer
neural networks and kernel methods.
