  Machine Learning algorithms are typically regarded as appropriate
optimization schemes for minimizing risk functions that are constructed on the
training set, which conveys statistical flavor to the corresponding learning
problem. When the focus is shifted on perception, which is inherently
interwound with time, recent alternative formulations of learning have been
proposed that rely on the principle of Least Cognitive Action, which very much
reminds us of the Least Action Principle in mechanics. In this paper, we
discuss different forms of the cognitive action and show the well-posedness of
learning. In particular, unlike the special case of the action in mechanics,
where the stationarity is typically gained on saddle points, we prove the
existence of the minimum of a special form of cognitive action, which yields
forth-order differential equations of learning. We also briefly discuss the
dissipative behavior of these equations that turns out to characterize the
process of learning.
