ImitationFlow: Learning Deep Stable Stochastic Dynamic Systems by Normalizing Flows

TL;DR

ImitationFlow is a deep generative model that learns complex, globally stable stochastic nonlinear dynamics by extending normalizing flows to stochastic differential equations, with proven stability and improved accuracy.

Contribution

It introduces a novel approach to learn stable stochastic differential equations from demonstrations, surpassing existing methods in stability and representation accuracy.

Findings

Proves Lyapunov stability for a class of stochastic differential equations.

Outperforms previous algorithms in representation accuracy.

Demonstrates effectiveness on standard datasets and real robot experiments.

Abstract

We introduce ImitationFlow, a novel Deep generative model that allows learning complex globally stable, stochastic, nonlinear dynamics. Our approach extends the Normalizing Flows framework to learn stable Stochastic Differential Equations. We prove the Lyapunov stability for a class of Stochastic Differential Equations and we propose a learning algorithm to learn them from a set of demonstrated trajectories. Our model extends the set of stable dynamical systems that can be represented by state-of-the-art approaches, eliminates the Gaussian assumption on the demonstrations, and outperforms the previous algorithms in terms of representation accuracy. We show the effectiveness of our method with both standard datasets and a real robot experiment.