Hierarchical Decomposition of Nonlinear Dynamics and Control for System Identification and Policy Distillation

TL;DR

This paper introduces a hierarchical approach to decompose complex nonlinear dynamics into simpler switching linear systems, enhancing interpretability and enabling extraction of local controllers from expert demonstrations.

Contribution

It applies hybrid switching system principles and probabilistic graphical models to decompose nonlinear dynamics and derive hierarchical controllers for imitation learning.

Findings

Decomposes nonlinear dynamics into stochastic switching linear systems.

Enables extraction of hierarchical controllers from expert data.

Uses EM algorithm for learning sequence models.

Abstract

The control of nonlinear dynamical systems remains a major challenge for autonomous agents. Current trends in reinforcement learning (RL) focus on complex representations of dynamics and policies, which have yielded impressive results in solving a variety of hard control tasks. However, this new sophistication and extremely over-parameterized models have come with the cost of an overall reduction in our ability to interpret the resulting policies. In this paper, we take inspiration from the control community and apply the principles of hybrid switching systems in order to break down complex dynamics into simpler components. We exploit the rich representational power of probabilistic graphical models and derive an expectation-maximization (EM) algorithm for learning a sequence model to capture the temporal structure of the data and automatically decompose nonlinear dynamics into stochastic switching linear dynamical systems. Moreover, we show how this framework of switching models enables extracting hierarchies of Markovian and auto-regressive locally linear controllers from nonlinear experts in an imitation learning scenario.