Safe Model-based Reinforcement Learning with Stability Guarantees (1705.08551v3)

Abstract: Reinforcement learning is a powerful paradigm for learning optimal policies from experimental data. However, to find optimal policies, most reinforcement learning algorithms explore all possible actions, which may be harmful for real-world systems. As a consequence, learning algorithms are rarely applied on safety-critical systems in the real world. In this paper, we present a learning algorithm that explicitly considers safety, defined in terms of stability guarantees. Specifically, we extend control-theoretic results on Lyapunov stability verification and show how to use statistical models of the dynamics to obtain high-performance control policies with provable stability certificates. Moreover, under additional regularity assumptions in terms of a Gaussian process prior, we prove that one can effectively and safely collect data in order to learn about the dynamics and thus both improve control performance and expand the safe region of the state space. In our experiments, we show how the resulting algorithm can safely optimize a neural network policy on a simulated inverted pendulum, without the pendulum ever falling down.

• The paper presents a novel RL algorithm that embeds Lyapunov functions to certify stability and enforce safety during exploration.
• It iteratively expands the region of attraction by constructing high-probability confidence intervals using Gaussian process models.
• Numerical experiments on an inverted pendulum demonstrate significant safe region expansion and improved control policy performance.

Safe Model-Based Reinforcement Learning with Stability Guarantees

Introduction

The paper "Safe Model-Based Reinforcement Learning with Stability Guarantees" by Felix Berkenkamp, Matteo Turchetta, Angela P. Schoellig, and Andreas Krause addresses the critical challenge of ensuring safety in reinforcement learning (RL) applications, particularly for real-world, safety-critical systems. Traditional RL algorithms focus on long-term gains through exploration, often at the expense of immediate safety—a trade-off unacceptable in systems such as autonomous vehicles or medical devices. To address this gap, the authors propose a novel RL algorithm that integrates safety constraints based on stability guarantees, particularly leveraging Lyapunov functions from control theory.

Reinforcement Learning and Safety

While RL has demonstrated remarkable success in controlled environments such as games, its application to real-world systems is limited due to safety concerns. In safety-critical systems, it is paramount to ensure that the actions taken to explore and learn do not compromise the system's stability or lead to harmful outcomes. The authors tackle this issue by embedding stability guarantees within the RL framework, ensuring that the learning process maintains the system within a safe operating region.

Methodology

The core innovation in this work is the integration of control-theoretic stability verification methods with statistical learning models to create a safe RL algorithm for continuous state-action spaces. Key to this methodology is the use of Lyapunov functions to certify the stability of the control policies. The paper extends traditional Lyapunov stability results, incorporating Gaussian process (GP) models to handle the system dynamics' uncertainties.

Problem Formulation

The system under consideration is a discrete-time dynamic system characterized by states and control actions. The true system dynamics are modeled as a combination of a known prior model and unknown model errors. The goal is to learn a control policy that minimizes cumulative costs while ensuring that intermediate policies do not lead to unsafe states.

Stability and Lyapunov Functions

The authors employ Lyapunov functions to define a region of attraction, a subset of the state space where the system trajectories remain stable and converge to a goal state. This approach relies on constructing high-probability confidence intervals on the Lyapunov function's decrease condition, ensuring that the system remains within the region of attraction during the learning process.

Safe Policy Optimization

The algorithm starts with an initial, safe policy and iteratively improves it. At each step, the region of attraction is estimated, and the policy is adapted to expand this region safely. The main steps are:

1. Computing a discretized version of the state space.
2. Constructing confidence intervals for the GP model of the dynamics.
3. Verifying the Lyapunov decrease condition on the discretized domain.
4. Optimizing the policy within the safe region and updating the region of attraction.

The authors implement safety guarantees by ensuring that all exploratory actions do not drive the system outside the estimated safe region.

Exploration Strategy

Given the statistical model's posterior uncertainty, the exploration strategy aims to reduce this uncertainty effectively. The algorithm selects the most informative state-action pairs within the current safe set, guided by the GP model's confidence intervals. This targeted exploration reduces model uncertainty and enhances policy performance while maintaining safety.

Numerical Results

The authors validate their approach using a simulated inverted pendulum, a standard control systems benchmark. The initial policy, based on a simplified dynamic model, has a small region of attraction and suboptimal performance. By applying their algorithm:

1. The region of attraction expands significantly, ensuring stability over a wider range of states.
2. The policy's performance improves, stabilizing the pendulum more effectively.

The results demonstrate the feasibility of safe learning, where all data points collected during learning are guaranteed to be within a safe region.

Implications and Future Directions

The proposed methodology provides a robust framework for integrating safety into model-based RL. Theoretically, it bridges the gap between control theory and RL, offering a pathway to deploy RL in safety-critical applications without compromising stability. Practically, it paves the way for applications in autonomous driving, robotics, and aerospace, where safety cannot be sacrificed for learning efficiency.

Future research could explore more sophisticated models for uncertainty quantification and adapt the methodology to a broader class of dynamic systems. Additionally, scaling the approach to higher-dimensional state spaces remains an open challenge, warranting further investigation into adaptive discretization and real-time policy adaptation mechanisms.

Conclusion

This paper makes a substantial contribution to the field of safe RL by integrating Lyapunov-based stability guarantees with model-based policy optimization. The proposed algorithm effectively balances exploration and safety, ensuring that the learning process does not jeopardize the system's stability. This work represents a vital step towards making RL applicable to real-world, safety-critical systems, with both immediate practical applications and significant theoretical implications.