Continual Learning through Hamilton Equations

Learning in a continual manner is one of the main challenges that the machine learning community is currently facing. The importance of the problem can be readily understood as soon as we consider settings where an agent is supposed to learn through an online interaction with a data stream, rather than operating offline on previously prepared data collections. In the last few years many efforts have been spent in proposing both models and algorithms to let machines learn in a continual manner, and the problem still remains extremely challenging. Many of the existing works rely on re-adapting the usual learning framework inherited from classic statistical approaches, that are typical of non-continual-learning oriented problems. In this paper we consider a fully new perspective, rethinking the methodologies to be used to tackle continual learning, instead of re-adapting offline-oriented optimization. In particular, we propose a novel method to frame continual and online learning within the framework of optimal control. The proposed formulation leads to a novel interpretation of learning dynamics in terms of Hamilton equations. As a case study for the theory, we consider the problem of unsupervised optical flow estimation from a video stream. An experimental proof of concept for this learning task is discussed with the purpose of illustrating the soundness of the proposed approach, and opening to further research in this direction.