Learning-based Model Predictive Control for Safe Exploration (1803.08287v3)

Abstract: Learning-based methods have been successful in solving complex control tasks without significant prior knowledge about the system. However, these methods typically do not provide any safety guarantees, which prevents their use in safety-critical, real-world applications. In this paper, we present a learning-based model predictive control scheme that can provide provable high-probability safety guarantees. To this end, we exploit regularity assumptions on the dynamics in terms of a Gaussian process prior to construct provably accurate confidence intervals on predicted trajectories. Unlike previous approaches, we do not assume that model uncertainties are independent. Based on these predictions, we guarantee that trajectories satisfy safety constraints. Moreover, we use a terminal set constraint to recursively guarantee the existence of safe control actions at every iteration. In our experiments, we show that the resulting algorithm can be used to safely and efficiently explore and learn about dynamic systems.

• The paper introduces SafeMPC, a method that integrates Gaussian Processes with MPC to provide high-probability safety guarantees in learning-based control systems.
• It employs an uncertainty-aware approach that balances exploration and exploitation using statistically derived confidence intervals from the GP model.
• Experimental results on an inverted pendulum validate its effectiveness in maintaining safety while optimizing performance during system exploration.

Learning-based Model Predictive Control for Safe Exploration

The paper authored by Torsten Koller, Felix Berkenkamp, Matteo Turchetta, and Andreas Krause introduces a novel method for managing safety in learning-based control systems, specifically through a Model Predictive Control (MPC) framework. This method, termed SafeMPC, is designed to ensure safety in situations where the system dynamics are not fully known and are being learned through interaction with the environment. The paper's core proposition is an uncertainty-aware approach to exploring and controlling dynamic systems, balancing the trade-offs between exploration (learning about the system) and exploitation (achieving optimal control performance).

Core Contribution

SafeMPC addresses a significant challenge in model-based reinforcement learning: the provision for safety assurances while investigating unknown systems. Traditional methods in this domain often lack safety guarantees, rendering them less useful in critical applications, such as autonomous vehicles or medical robotics, where erratic behavior can have severe consequences. The key to SafeMPC's approach is leveraging Gaussian processes (GPs) to model system dynamics, not only capturing the uncertainties in a computationally feasible way but also using these models to ensure that the system remains within safe operating bounds with high probability.

Methodological Details

The methodology hinges on three integral components:

1. Model Learning with Gaussian Processes: SafeMPC uses GPs to predict future states of the system with quantified uncertainty. By understanding the model error within bounded confidence levels, SafeMPC manages the risk associated with exploration.
2. Safe Control through MPC: The algorithm constructs a series of control inputs using MPC that respect state and input constraints while considering statistical confidence intervals derived from the GP model. This results in the formulation of trajectories that are recursively feasible within a high probability of safety.
3. Terminal Set Constraint: An essential theoretical safeguard is the terminal constraint that ensures the system can steer back to a predetermined safe region, thereby recursively satisfying feasibility requirements.

Experimental Evaluation

The experiments conducted, particularly on an inverted pendulum system, validate the efficiency of SafeMPC in balancing exploration and performance without breaching safety constraints. It is shown that SafeMPC effectively enhances learning by optimally selecting trajectories that maximize information gain while maintaining safety, suggesting its potential applicability to more complex, real-world systems.

Implications and Future Work

The introduction of SafeMPC contributes significantly to the field of safe reinforcement learning by offering a robust framework that can adapt to and learn about dynamic environments while providing assurances against unsafe operations. The implications of this work extend beyond theoretical constructs, offering practical guidelines for developing safe artificial intelligence systems used in contexts where failure is not an option.

Future research could explore further optimization of trajectory planning, such as adaptive horizon lengths based on the current knowledge state or integrating online adaptation mechanisms within the MPC framework to handle dynamic, non-stationary environments more effectively. Incorporating these advancements could broaden the SafeMPC framework's applicability to more complex and high-dimensional tasks encountered in advanced autonomous systems.

The research presented suggests a promising frontier in ensuring that AI systems—particularly those deployed in safety-critical roles—do not only learn efficiently but also operate safely within uncertain environments.