  In this paper, we introduce Path Integral Networks (PI-Net), a recurrent
network representation of the Path Integral optimal control algorithm. The
network includes both system dynamics and cost models, used for optimal control
based planning. PI-Net is fully differentiable, learning both dynamics and cost
models end-to-end by back-propagation and stochastic gradient descent. Because
of this, PI-Net can learn to plan. PI-Net has several advantages: it can
generalize to unseen states thanks to planning, it can be applied to continuous
control tasks, and it allows for a wide variety learning schemes, including
imitation and reinforcement learning. Preliminary experiment results show that
PI-Net, trained by imitation learning, can mimic control demonstrations for two
simulated problems; a linear system and a pendulum swing-up problem. We also
show that PI-Net is able to learn dynamics and cost models latent in the
demonstrations.
