Energy-Based Continuous Inverse Optimal Control

TL;DR

This paper introduces an energy-based framework for continuous inverse optimal control, learning cost functions from expert trajectories using maximum likelihood, Langevin dynamics, and cooperative training with a trajectory generator, demonstrated on autonomous driving.

Contribution

It proposes a novel energy-based model approach for inverse optimal control, combining sampling and optimization, with a cooperative training scheme for efficiency, applied to autonomous driving tasks.

Findings

Effective learning of cost functions from expert data.

Improved efficiency through cooperative training with a trajectory generator.

Successful application to autonomous driving scenarios.

Abstract

The problem of continuous inverse optimal control (over finite time horizon) is to learn the unknown cost function over the sequence of continuous control variables from expert demonstrations. In this article, we study this fundamental problem in the framework of energy-based model, where the observed expert trajectories are assumed to be random samples from a probability density function defined as the exponential of the negative cost function up to a normalizing constant. The parameters of the cost function are learned by maximum likelihood via an "analysis by synthesis" scheme, which iterates (1) synthesis step: sample the synthesized trajectories from the current probability density using the Langevin dynamics via back-propagation through time, and (2) analysis step: update the model parameters based on the statistical difference between the synthesized trajectories and the observed trajectories. Given the fact that an efficient optimization algorithm is usually available for an optimal control problem, we also consider a convenient approximation of the above learning method, where we replace the sampling in the synthesis step by optimization. Moreover, to make the sampling or optimization more efficient, we propose to train the energy-based model simultaneously with a top-down trajectory generator via cooperative learning, where the trajectory generator is used to fast initialize the synthesis step of the energy-based model. We demonstrate the proposed methods on autonomous driving tasks, and show that they can learn suitable cost functions for optimal control.