Model agnostic methods meta-learn despite misspecifications

Due to its empirical success on few shot classification and reinforcement learning, meta-learning recently received a lot of interest. Meta-learning leverages data from previous tasks to quickly learn a new task, despite limited data. In particular, model agnostic methods look for initialisation points from which gradient descent quickly adapts to any new task. Although it has been empirically suggested that such methods learn a good shared representation during training, there is no strong theoretical evidence of such behavior. More importantly, it is unclear whether these methods truly are model agnostic, i.e., whether they still learn a shared structure despite architecture misspecifications. To fill this gap, this work shows in the limit of an infinite number of tasks that first order ANIL with a linear two-layer network architecture successfully learns a linear shared representation. Moreover, this result holds despite misspecifications: having a large width with respect to the hidden dimension of the shared representation does not harm the algorithm performance. The learnt parameters then allow to get a small test loss after a single gradient step on any new task. Overall this illustrates how well model agnostic methods can adapt to any (unknown) model structure.