Decomposing Control Lyapunov Functions for Efficient Reinforcement Learning

Core Concepts

Using Decomposed Control Lyapunov Functions can reduce sample complexity and improve RL performance.

Abstract

The content discusses the application of Control Lyapunov Functions (CLF) in Reinforcement Learning (RL) to reduce sample complexity. It introduces Decomposed Control Lyapunov Functions (DCLFs) as a method to address high-dimensional systems, improving RL performance through reward shaping. The paper outlines system decomposition techniques, CLVF computation, and incorporation into standard RL algorithms. Experiments on Dubins Car, Lunar Lander, and Drone simulations demonstrate the effectiveness of DCLFs in accelerating policy learning with reduced data requirements. I. Introduction RL for autonomous robots in complex environments. Challenges due to nonlinear dynamics and incomplete information. Data-driven approaches like RL require extensive data sets. II. Related Work Prior work on reducing sample complexity in RL. Incorporating optimal control methods with RL. Reward shaping techniques for faster policy convergence. III. Preliminaries Definition of CLF and its stability properties. Discrete-time system representation for value function computation. Hamilton-Jacobi Reachability analysis for safety formulation. IV. Decomposed Control Lyapunov Value Functions System decomposition technique for high-dimensional systems. Computation of DCLFs using CLVFs from subsystems. Incorporation of DCLFs into standard RL algorithms for reward shaping. V. Results Dubins Car Experiment: Comparison between SAC+DCLF and SAC baselines. Convergence achieved with reduced data requirements using DCLF. Lunar Lander Experiment: Application of DCLF in SAC and PPO algorithms. Improved performance compared to standard algorithms. Drone Experiment: Utilizing DCLF with SAC algorithm for efficient policy learning. Reduced training time and improved convergence compared to baselines. VI. Conclusions and Future Work Extension of CLF computation to other decompositions. Analysis of DCLF sensitivity to modeling errors. Future research directions for broader applications in robotics.

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Quotes

"Data-driven approaches are used to account for uncertainties in the model." "A recent approach addresses the high-sample complexity of RL algorithms by introducing a Control Lyapunov Function (CLF)." "Our approach allows using a smaller discount factor and finds policies with less data."

Key Insights Distilled From

Decomposing Control Lyapunov Functions for Efficient Reinforcement Learning

by Antonio Lope... at arxiv.org 03-20-2024

https://arxiv.org/pdf/2403.12210.pdf

Deeper Inquiries

How can the concept of DCLFs be extended to more general decompositions

To extend the concept of Decomposed Control Lyapunov Functions (DCLFs) to more general decompositions, we can explore techniques that allow for subsystems with shared controls. Currently, the method presented in the context focuses on decomposing systems where states are coupled but not necessarily through shared controls. By developing algorithms or frameworks that can handle shared control scenarios within a decomposition, we can apply DCLFs to a broader range of systems. This extension would involve addressing how different subsystems interact when sharing control inputs and ensuring that each subsystem's dynamics are well-defined and independent within the overall system.

What are the implications of assuming an accurate dynamics model for implementing DCLFs

Assuming an accurate dynamics model is crucial for implementing DCLFs as it forms the foundation for system decomposition and subsequent CLVF computation. Inaccuracies in the model could lead to incorrect partitioning of subsystems or inaccurate CLVFs, impacting the stability analysis and reward shaping process in reinforcement learning algorithms. Therefore, robust methods for verifying model accuracy should be integrated into the implementation of DCLFs. Techniques such as sensitivity analysis, uncertainty quantification, or validation against real-world data can help assess model fidelity before applying DCLFs in RL settings.

How can the sensitivity of DCLFs to errors in system modeling be mitigated effectively

The sensitivity of Decomposed Control Lyapunov Functions (DCLFs) to errors in system modeling can be effectively mitigated through several strategies: Uncertainty Quantification: Incorporating uncertainty estimates into the modeling process allows for quantifying potential errors and their impact on DCLF computations. Robust Optimization: Implementing robust optimization techniques that account for variations or uncertainties in system parameters can enhance the resilience of DCLF-based RL algorithms. Model Validation: Conducting thorough validation tests by comparing simulation results with real-world data helps identify discrepancies between modeled and actual system behavior. Adaptive Learning: Integrating adaptive learning mechanisms that adjust DCLF formulations based on online feedback from system interactions enables dynamic adaptation to changing conditions or inaccuracies. Ensemble Modeling: Employing ensemble models that capture multiple plausible representations of system dynamics provides a more comprehensive view and reduces reliance on a single potentially flawed model. By combining these approaches tailored to address specific sources of error in system modeling, practitioners can enhance the reliability and effectiveness of using DCLFs in reinforcement learning applications despite inherent uncertainties present in complex dynamical systems."