SINDy-RL: Interpretable and Efficient Model-Based Reinforcement Learning (2403.09110v1)

Abstract: Deep reinforcement learning (DRL) has shown significant promise for uncovering sophisticated control policies that interact in environments with complicated dynamics, such as stabilizing the magnetohydrodynamics of a tokamak fusion reactor or minimizing the drag force exerted on an object in a fluid flow. However, these algorithms require an abundance of training examples and may become prohibitively expensive for many applications. In addition, the reliance on deep neural networks often results in an uninterpretable, black-box policy that may be too computationally expensive to use with certain embedded systems. Recent advances in sparse dictionary learning, such as the sparse identification of nonlinear dynamics (SINDy), have shown promise for creating efficient and interpretable data-driven models in the low-data regime. In this work we introduce SINDy-RL, a unifying framework for combining SINDy and DRL to create efficient, interpretable, and trustworthy representations of the dynamics model, reward function, and control policy. We demonstrate the effectiveness of our approaches on benchmark control environments and challenging fluids problems. SINDy-RL achieves comparable performance to state-of-the-art DRL algorithms using significantly fewer interactions in the environment and results in an interpretable control policy orders of magnitude smaller than a deep neural network policy.

• The paper introduces SINDy-RL, a novel framework that integrates sparse identification of nonlinear dynamics into reinforcement learning, achieving up to 100x improvement in sample efficiency over traditional methods.
• The methodology employs a Dyna-style algorithm that fits an ensemble of sparse symbolic models to surrogate dynamics, significantly reducing data requirements and computational costs.
• Results across benchmark tasks like cartpole swing-up and Swimmer-v4 demonstrate that SINDy-RL delivers robust, compact, and interpretable control policies for complex systems.

Interpretable and Efficient Control Policies with SINDy-RL in Reinforcement Learning

The paper under analysis explores the integration of sparse identification of nonlinear dynamics (SINDy) into the reinforcement learning (RL) framework, specifically addressing inefficiencies in deep reinforcement learning (DRL) methods. Notably, DRL, while effective in deriving complex control policies for environments with intricate dynamics, often encounters limitations related to high sample complexity and lack of interpretability. In response, the authors propose the SINDy-RL framework, aiming to leverage the strengths of both model-based and model-free approaches to enhance efficiency and interpretability in RL applications.

SINDy-RL seeks to address three core limitations associated with traditional DRL approaches: excessive data requirements, resource-intensive deployment, and "black-box" models lacking transparency. In doing so, it presents significant advancements in areas where computational resources, interpretability, and sample efficiency are critical constraints. The approach integrates SINDy, a recent breakthrough in sparse dictionary learning recognized for producing interpretable models in data-sparse regimes, within a reinforcement learning context to derive efficient and compact representations of environment dynamics, reward functions, and control policies.

Method Overview

The methodology presented revolves around a Dyna-style model-based reinforcement learning algorithm that employs SINDy to learn sparse, symbolic models of environment dynamics and, when necessary, the reward functions. A pivotal attribute of the SINDy-RL is its sample-efficient exploration, facilitated by the surrogate dynamics model, which aids in both training and deploying lightweight policies.

Key procedural elements involve initially fitting an ensemble of SINDy models to establish a surrogate approximation of the environment dynamics, which serve as a platform for DRL policy optimization. Iteratively, policies trained in the surrogate environments are updated using model-free techniques and then tested within the original environment to improve upon the learned dynamics iteratively. The ensemble approach to the dictionary models offers intrinsic robustness, ensuring convergence even in the presence of noise or sparse data availability.

Results and Numerical Findings

The efficacy of SINDy-RL is demonstrated across various benchmark environments, such as the dm cartpole 'swing-up', the OpenAI gymnasium Swimmer-v4, and the HydroGym Cylinder flow scenarios. Remarkably, the proposed SINDy-RL exhibits a hundredfold improvement in sample efficiency for the swing-up task compared to traditional PPO-based policies, underlining its capacity to operate in a constrained data scenario effectively.

Notably, in the context of complex systems such as fluid mechanics, the application of SINDy principles allows the derivation of surrogate reward functions where the exact reward is challenging to measure, thus facilitating efficient policy training in such partially observed environments.

In addition to its numerical performance, the use of SINDy further enables a significant reduction in model complexity, providing the capability to deploy interpretable control policies that are orders of magnitude more compact than their deep network counterparts, enhancing their usability in resource-constrained environments.

Implications and Future Prospects

The implications of SINDy-RL are profound, offering a pathway to leverage interpretability alongside efficiency in dynamic system control. The integration of symbolic policy representations provides researchers and practitioners with a tool to understand and trust the derived policies, crucial for deploying such systems in safety-critical applications.

Future developments in AI could potentially revolve around refining the surrogate dynamics integration, enhancing stability, and exploring broader applications in partially observed settings. Additionally, this work opens up avenues for further automating the process of selecting and optimizing dictionary libraries to account for diverse environment types while maintaining computational tractability.

Overall, SINDy-RL represents a promising intersection of model-based and model-free reinforcement learning, setting the stage for a new breed of RL algorithms that are efficient, interpretable, and robust in data-scarce regimes.