Learning Contraction Policies from Offline Data

TL;DR

This paper introduces a data-driven approach to learn convergent control policies for robots from offline data by jointly learning the policy and contraction metric using a learned dynamics model, leading to faster and more robust convergence.

Contribution

It proposes a novel method to learn contraction policies and metrics jointly from offline data, including a data augmentation technique using a learned dynamics model.

Findings

Enforcing contraction improves convergence speed.

The method enhances robustness of the learned policies.

Successful application on simulated robotic tasks.

Abstract

This paper proposes a data-driven method for learning convergent control policies from offline data using Contraction theory. Contraction theory enables constructing a policy that makes the closed-loop system trajectories inherently convergent towards a unique trajectory. At the technical level, identifying the contraction metric, which is the distance metric with respect to which a robot's trajectories exhibit contraction is often non-trivial. We propose to jointly learn the control policy and its corresponding contraction metric while enforcing contraction. To achieve this, we learn an implicit dynamics model of the robotic system from an offline data set consisting of the robot's state and input trajectories. Using this learned dynamics model, we propose a data augmentation algorithm for learning contraction policies. We randomly generate samples in the state-space and propagate them forward in time through the learned dynamics model to generate auxiliary sample trajectories. We then learn both the control policy and the contraction metric such that the distance between the trajectories from the offline data set and our generated auxiliary sample trajectories decreases over time. We evaluate the performance of our proposed framework on simulated robotic goal-reaching tasks and demonstrate that enforcing contraction results in faster convergence and greater robustness of the learned policy.