  Trial-and-error learning requires evaluating variable actions and reinforcing
successful variants. In songbirds, vocal exploration is induced by LMAN, the
output of a basal ganglia-circuit that also contributes a corrective bias to
the vocal output. This bias is gradually consolidated in RA, a motor cortex
analogue downstream of LMAN. We develop a new model of such two-stage learning.
Using stochastic gradient descent, we derive how the activity in 'tutor'
circuits (e.g., LMAN) should match plasticity mechanisms in 'student' circuits
(e.g., RA) to achieve efficient learning. We further describe a reinforcement
learning framework through which the tutor can build its teaching signal. We
show that mismatches between the tutor signal and the plasticity mechanism can
impair learning. Applied to birdsong, our results predict the temporal
structure of the corrective bias from LMAN given a plasticity rule in RA. Our
framework can be applied predictively to other paired brain areas showing
two-stage learning.
