  This work establishes that a physical system can perform statistical learning
without gradient computations, via an Agnostic Equilibrium Propagation
(Aeqprop) procedure that combines energy minimization, homeostatic control, and
nudging towards the correct response. In Aeqprop, the specifics of the system
do not have to be known: the procedure is based only on external manipulations,
and produces a stochastic gradient descent without explicit gradient
computations. Thanks to nudging, the system performs a true, order-one gradient
step for each training sample, in contrast with order-zero methods like
reinforcement or evolutionary strategies, which rely on trial and error. This
procedure considerably widens the range of potential hardware for statistical
learning to any system with enough controllable parameters, even if the details
of the system are poorly known. Aeqprop also establishes that in natural
(bio)physical systems, genuine gradient-based statistical learning may result
from generic, relatively simple mechanisms, without backpropagation and its
requirement for analytic knowledge of partial derivatives.
