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Sample-efficient diffusion-based control of complex nonlinear systems

Hongyi Chen, Jingtao Ding, Jianhai Shu, Xinchun Yu, Xiaojun Liang, Yong Li, Xiao-Ping Zhang

TL;DR

This work tackles the problem of sample-efficient control for complex nonlinear systems by reframing control as diffusion-based trajectory generation conditioned on start and goal states. It introduces SEDC, with three innovations—Decoupled State Diffusion (DSD), Dual-Mode Decomposition (DMD), and Guided Self-finetuning (GSF)—to address high-dimensional state-action spaces, strong nonlinearity, and non-optimal offline data. Across Burgers, Kuramoto, and Inverted Pendulum, SEDC achieves 39.5-49.4% better Target Loss than baselines and matches full-data performance using only 10% of the data, while reducing energy costs. These results highlight improved data efficiency, trajectory feasibility, and convergence toward near-optimal control policies in nonlinear dynamics.

Abstract

Complex nonlinear system control faces challenges in achieving sample-efficient, reliable performance. While diffusion-based methods have demonstrated advantages over classical and reinforcement learning approaches in long-term control performance, they are limited by sample efficiency. This paper presents SEDC (Sample-Efficient Diffusion-based Control), a novel diffusion-based control framework addressing three core challenges: high-dimensional state-action spaces, nonlinear system dynamics, and the gap between non-optimal training data and near-optimal control solutions. Through three innovations - Decoupled State Diffusion, Dual-Mode Decomposition, and Guided Self-finetuning - SEDC achieves 39.5\%-49.4\% better control accuracy than baselines while using only 10\% of the training samples, as validated across three complex nonlinear dynamic systems. Our approach represents a significant advancement in sample-efficient control of complex nonlinear systems. The implementation of the code can be found at https://anonymous.4open.science/r/DIFOCON-C019.

Sample-efficient diffusion-based control of complex nonlinear systems

TL;DR

This work tackles the problem of sample-efficient control for complex nonlinear systems by reframing control as diffusion-based trajectory generation conditioned on start and goal states. It introduces SEDC, with three innovations—Decoupled State Diffusion (DSD), Dual-Mode Decomposition (DMD), and Guided Self-finetuning (GSF)—to address high-dimensional state-action spaces, strong nonlinearity, and non-optimal offline data. Across Burgers, Kuramoto, and Inverted Pendulum, SEDC achieves 39.5-49.4% better Target Loss than baselines and matches full-data performance using only 10% of the data, while reducing energy costs. These results highlight improved data efficiency, trajectory feasibility, and convergence toward near-optimal control policies in nonlinear dynamics.

Abstract

Complex nonlinear system control faces challenges in achieving sample-efficient, reliable performance. While diffusion-based methods have demonstrated advantages over classical and reinforcement learning approaches in long-term control performance, they are limited by sample efficiency. This paper presents SEDC (Sample-Efficient Diffusion-based Control), a novel diffusion-based control framework addressing three core challenges: high-dimensional state-action spaces, nonlinear system dynamics, and the gap between non-optimal training data and near-optimal control solutions. Through three innovations - Decoupled State Diffusion, Dual-Mode Decomposition, and Guided Self-finetuning - SEDC achieves 39.5\%-49.4\% better control accuracy than baselines while using only 10\% of the training samples, as validated across three complex nonlinear dynamic systems. Our approach represents a significant advancement in sample-efficient control of complex nonlinear systems. The implementation of the code can be found at https://anonymous.4open.science/r/DIFOCON-C019.

Paper Structure

This paper contains 29 sections, 21 equations, 5 figures, 7 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Works
  3. Backgrounds
  4. Problem Setting
  5. Diffusion Model
  6. SEDC: the Proposed Method
  7. Decoupled State Diffusion (DSD)
  8. Dual Mode Decomposition (DMD) for Denoising Module
  9. Guided Self-finetuning (GSF)
  10. Experiments
  11. Overall Control Performance
  12. Sample Efficiency
  13. Ablation Study
  14. Conclusion
  15. Algorithm form of SEDC
  16. ...and 14 more sections

Figures (5)

  • Figure 1: Illustration of SEDC, the proposed conditional diffusion-based controller.
  • Figure 2: Comparison of target loss and energy cost $J$ across different datasets. The closer the data point is to the bottom left, the better the performance.
  • Figure 3: Sample-efficiency comparison on Burgers, Kuramoto and Inverse Pendulum dynamics.
  • Figure 4: Comparison of State Trajectory Consistency between SEDC and w/o DSD Models. The heatmaps show induced states (left), sampled states (middle), and their absolute differences (right) for both SEDC (top) and w/o DSD (bottom) approaches under identical start-target conditions.
  • Figure 5: Comparison of different methods on Burgers, Kuramoto and Inverse Pendulum systems