  Humans and other animals are capable of improving their learning performance
as they solve related tasks from a given problem domain, to the point of being
able to learn from extremely limited data. While synaptic plasticity is
generically thought to underlie learning in the brain, the precise neural and
synaptic mechanisms by which learning processes improve through experience are
not well understood. Here, we present a general-purpose, biologically-plausible
meta-learning rule which estimates gradients with respect to the parameters of
an underlying learning algorithm by simply running it twice. Our rule may be
understood as a generalization of contrastive Hebbian learning to meta-learning
and notably, it neither requires computing second derivatives nor going
backwards in time, two characteristic features of previous gradient-based
methods that are hard to conceive in physical neural circuits. We demonstrate
the generality of our rule by applying it to two distinct models: a complex
synapse with internal states which consolidate task-shared information, and a
dual-system architecture in which a primary network is rapidly modulated by
another one to learn the specifics of each task. For both models, our
meta-learning rule matches or outperforms reference algorithms on a wide range
of benchmark problems, while only using information presumed to be locally
available at neurons and synapses. We corroborate these findings with a
theoretical analysis of the gradient estimation error incurred by our rule.
