This work establishes that a physical system can perform statistical learning without gradient computations, via an \emph{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 ...