We present a learning system which is able to quickly and reliably acquire a robust feedback control policy for 3D dynamic walking from a blank-slate using only trials implemented on our physical robot. The robot begins walking within a minute and learning converges in approximately 20 minutes. This success can be attributed to the mechanics of our robot, which are modeled after a passive dynamic walker, and to a dramatic reduction in the dimensionality of the learning problem. We reduce the dimensionality by designing a robot with only 6 internal degrees of freedom and 4 actuators, by decomposing the control system in the frontal and sagittal planes, and by formulating the learning problem on the discrete return map dynamics. We apply a stochastic policy gradient algorithm to this reduced problem and decrease the variance of the update using a state-based estimate of the expected cost. This optimized learning system works quickly enough that the robot is able to continually adapt to the terrain as it walks.