Scalable Learning of High-Dimensional Demonstrations with Composition of Linear Parameter Varying Dynamical Systems

2025-07-05

AI Summary

Learning stable dynamics from high-dimensional demonstration data faces challenges including non-convex bilinear matrix inequality (BMI) optimization, high computational cost, and numerical instability. To address these, this paper proposes a scalable linear parameter-varying (LPV) dynamics composition framework. By constructing a piecewise-affine LPV model and introducing slack variables with structural constraints, the original non-convex BMI problem is decomposed into a sequence of convex linear matrix inequality (LMI) subproblems, each amenable to efficient interior-point solvers. This reformulation drastically reduces computational complexity, enabling real-time learning and generalization in high-dimensional state spaces. Experiments on robotic manipulation tasks demonstrate that the proposed method achieves superior stability guarantees, modeling accuracy, and training efficiency compared to baseline approaches, while significantly mitigating numerical ill-conditioning inherent in conventional BMI solvers.

Technology Category

• Intelligent Robots: State Estimation
• Search and Optimization: Learning to Search
• Planning, Routing, and Scheduling: Learning for Planning and Scheduling

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

Abstract

Learning from Demonstration (LfD) techniques enable robots to learn and generalize tasks from user demonstrations, eliminating the need for coding expertise among end-users. One established technique to implement LfD in robots is to encode demonstrations in a stable Dynamical System (DS). However, finding a stable dynamical system entails solving an optimization problem with bilinear matrix inequality (BMI) constraints, a non-convex problem which, depending on the number of scalar constraints and variables, demands significant computational resources and is susceptible to numerical issues such as floating-point errors. To address these challenges, we propose a novel compositional approach that enhances the applicability and scalability of learning stable DSs with BMIs.

Problem

• Learning stable dynamical systems from demonstrations efficiently
• Solving non-convex BMI constraints in optimization problems
• Enhancing scalability of high-dimensional DS learning

Innovation

• Compositional approach for stable DS learning
• Addresses BMI constraints via optimization
• Enhances scalability in high-dimensional demonstrations