Actively Learning Gaussian Process Dynamics (1911.09946v3)

Abstract: Despite the availability of ever more data enabled through modern sensor and computer technology, it still remains an open problem to learn dynamical systems in a sample-efficient way. We propose active learning strategies that leverage information-theoretical properties arising naturally during Gaussian process regression, while respecting constraints on the sampling process imposed by the system dynamics. Sample points are selected in regions with high uncertainty, leading to exploratory behavior and data-efficient training of the model. All results are finally verified in an extensive numerical benchmark.

• The paper proposes sample-efficient active learning strategies using information theory for Gaussian Process dynamics modeling.
• Key methods introduced include separated search and joint optimization approaches that leverage control inputs for informative data collection.
• Numerical benchmarks demonstrate that joint optimization strategies significantly improve model accuracy and state space coverage in various dynamic systems.

Actively Learning Gaussian Process Dynamics: An Overview

This paper addresses the challenge of learning dynamical systems in a sample-efficient manner, leveraging Gaussian Process (GP) regression. This approach is paramount given the constraints imposed on sampling due to system dynamics, which differentiates it from other machine learning endeavors where data can be collected more freely. The authors propose an active learning strategy that capitalizes on information-theoretical properties inherent in GP regression, aiming to enhance exploration and improve data efficiency during model training.

Key Contributions

The authors introduce several active learning strategies that aim to identify informative data points within the dynamics of Gaussian Processes for nonlinear system identification:

1. Separated Search and Control (sep): This method distinguishes the selection of informative points from the control inputs required to reach those points. While theoretical guarantees on suboptimality are provided, practical limitations are identified.
2. Joint Optimization Approaches: Two variants—receding horizon and plan and apply (rec and p&a)—are presented. These strategies simultaneously optimize control inputs and target states by leveraging an information criterion subject to dynamic constraints.

Problem Statement and Methodology

The paper formulates the active learning problem over discrete-time dynamics. A foundational aspect is how to excite the system to produce sample-efficient data for learning the unknown dynamics function, $f$, modeled by GP. The paper clearly illustrates the distinction from static learning problems, highlighting the necessity for steering system states through control inputs rather than independently querying data points.

The authors utilize differential entropy as a measure of uncertainty reduction in GP predictions, optimizing control inputs to achieve a more informative dataset. This moves beyond traditional static active learning methodologies, embedding a dynamic understand to address multidimensional challenges.

Numerical Benchmark

An exhaustive benchmark using various control system models demonstrates the comparative performance of the proposed methods:

• In systems such as the pendulum, unicycle, and the two-link robot, the joint optimization approaches yielded substantial improvements in both RMSE and state space coverage compared to standard methodologies and separated search methods.
• Notably, in more complex systems like the half-cheetah, utilizing optimization for exploration showcased statistically significant reductions in prediction error.

The authors provide a granular analysis of how computational burden impacts method efficacy, highlighting scenarios where batch processing advancements (p&a) might serve as a computationally feasible alternative to the receding horizon approach.

Implications and Future Work

The implications of this research are profound for advancing model learning and control in nonlinear dynamic systems, utilizing GPs. The adaptive nature of active learning methodologies proposed serve to optimize exploratory control signals while respecting system constraints, thus fostering more accurate system models with fewer data points.

Future directions may include examining the integration of noisy inputs and latent states within the GP framework, enhancing computational efficiency for real-time applications, and applying validated algorithms in hardware contexts. Additionally, the consideration of alternative cost functions could further refine the efficacy and versatility of active learning strategies.

Conclusion

This paper contributes valuable insights into sample-efficient active learning for Gaussian Process dynamics. By delineating separated search from informed control trajectories, the research offers a nuanced understanding that recognizes the unique challenges posed by dynamical systems. The methods proposed hold potential for substantial advancements in controlling complex systems, making this work a significant reference point for further exploration in active learning and GP applications in dynamical system modeling.