Differentiable MPC for End-to-end Planning and Control

TL;DR

This paper introduces a differentiable MPC framework that enables end-to-end reinforcement learning by differentiating through the KKT conditions, improving data efficiency and performance over traditional methods.

Contribution

It develops a novel approach to differentiate through MPC using KKT conditions, allowing joint learning of cost and dynamics in an end-to-end manner.

Findings

MPC policies are more data-efficient than neural networks.

The method outperforms traditional system identification in unrealizable expert settings.

Demonstrated effectiveness in pendulum and cartpole domains.

Abstract

We present foundations for using Model Predictive Control (MPC) as a differentiable policy class for reinforcement learning in continuous state and action spaces. This provides one way of leveraging and combining the advantages of model-free and model-based approaches. Specifically, we differentiate through MPC by using the KKT conditions of the convex approximation at a fixed point of the controller. Using this strategy, we are able to learn the cost and dynamics of a controller via end-to-end learning. Our experiments focus on imitation learning in the pendulum and cartpole domains, where we learn the cost and dynamics terms of an MPC policy class. We show that our MPC policies are significantly more data-efficient than a generic neural network and that our method is superior to traditional system identification in a setting where the expert is unrealizable.