Path Integral Networks: End-to-End Differentiable Optimal Control

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.