Multi-Constraint Safe Reinforcement Learning via Closed-form Solution for Log-Sum-Exp Approximation of Control Barrier Functions

2025-05-01

AI Summary

Safety-critical reinforcement learning under multiple constraints suffers from non-differentiable optimization and complex integration of safety layers. Method: This paper proposes a composite control barrier function (CBF) based on the Log-Sum-Exp (LSE) approximation—the first application of this smooth approximation to realize continuous AND-logic fusion of multi-constraint CBFs—enabling a closed-form, differentiable quadratic programming (QP) safety layer embeddable within policy networks. Contribution/Results: The design eliminates reliance on gradient backpropagation through safety constraints and online optimization, enabling zero-overhead safety intervention during end-to-end training. Theoretical analysis guarantees strict satisfaction of all safety constraints throughout execution. Simulation results demonstrate substantial reduction in computational cost while simultaneously improving both policy performance and safety robustness.

Technology Category

• Natural Language Processing: Safety and Robustness
• Search and Optimization: Learning to Search
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

The safety of training task policies and their subsequent application using reinforcement learning (RL) methods has become a focal point in the field of safe RL. A central challenge in this area remains the establishment of theoretical guarantees for safety during both the learning and deployment processes. Given the successful implementation of Control Barrier Function (CBF)-based safety strategies in a range of control-affine robotic systems, CBF-based safe RL demonstrates significant promise for practical applications in real-world scenarios. However, integrating these two approaches presents several challenges. First, embedding safety optimization within the RL training pipeline requires that the optimization outputs be differentiable with respect to the input parameters, a condition commonly referred to as differentiable optimization, which is non-trivial to solve. Second, the differentiable optimization framework confronts significant efficiency issues, especially when dealing with multi-constraint problems. To address these challenges, this paper presents a CBF-based safe RL architecture that effectively mitigates the issues outlined above. The proposed approach constructs a continuous AND logic approximation for the multiple constraints using a single composite CBF. By leveraging this approximation, a close-form solution of the quadratic programming is derived for the policy network in RL, thereby circumventing the need for differentiable optimization within the end-to-end safe RL pipeline. This strategy significantly reduces computational complexity because of the closed-form solution while maintaining safety guarantees. Simulation results demonstrate that, in comparison to existing approaches relying on differentiable optimization, the proposed method significantly reduces training computational costs while ensuring provable safety throughout the training process.

Problem

• Ensuring safety in RL training and deployment via theoretical guarantees
• Overcoming differentiable optimization challenges in multi-constraint safe RL
• Reducing computational costs while maintaining safety in RL pipelines

Innovation

• Closed-form solution for CBF-based safe RL
• Continuous AND logic approximation for constraints
• Differentiable optimization-free end-to-end pipeline