# Distributed Risk-Sensitive Safety Filters for Uncertain Discrete-Time Systems

arXiv: https://arxiv.org/abs/2506.07347 · HTML: https://mlsanity.com/paper/2506.07347/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 18 references that are in the map.
- First posted on arXiv 9 Jun 2025.

## Builds on (most cited first, 13 of 13)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Control Barrier Function Based Quadratic Programs for Safety Critical Systems](https://mlsanity.com/paper/1609.06408/) (2016)
- [Uniform Error Bounds for Gaussian Process Regression with Application to Safe Control](https://mlsanity.com/paper/1906.01376/) (2019)
- [How to Train Your Neural Control Barrier Function: Learning Safety Filters for Complex Input-Constrained Systems](https://mlsanity.com/paper/2310.15478/) (2023)
- [Safe Multi-Agent Interaction through Robust Control Barrier Functions with Learned Uncertainties](https://mlsanity.com/paper/2004.05273/) (2020)
- [Learning Safe Control for Multi-Robot Systems: Methods, Verification, and Open Challenges](https://mlsanity.com/paper/2311.13714/) (2023)
- [Safe Policy Synthesis in Multi-Agent POMDPs via Discrete-Time Barrier Functions](https://mlsanity.com/paper/1903.07823/) (2019)
- [Safety-Critical Control for Autonomous Systems: Control Barrier Functions via Reduced-Order Models](https://mlsanity.com/paper/2403.09865/) (2024)
- [Bridging the Sim-to-Real Gap with Bayesian Inference](https://mlsanity.com/paper/2403.16644/) (2024)
- [Discrete GCBF Proximal Policy Optimization for Multi-agent Safe Optimal Control](https://mlsanity.com/paper/2502.03640/) (2025)
- [Safe Reinforcement Learning via Confidence-Based Filters](https://mlsanity.com/paper/2207.01337/) (2022)
- [Robust Safety under Stochastic Uncertainty with Discrete-Time Control Barrier Functions](https://mlsanity.com/paper/2302.07469/) (2023)
- [Risk-Sensitive Inhibitory Control for Safe Reinforcement Learning](https://mlsanity.com/paper/2310.01538/) (2023)

## Abstract (arXiv)

Ensuring safety in multi-agent systems is a significant challenge, particularly in settings where centralized coordination is impractical. In this work, we propose a novel risk-sensitive safety filter for discrete-time multi-agent systems with uncertain dynamics that leverages control barrier functions (CBFs) defined through value functions. Our approach relies on centralized risk-sensitive safety conditions based on exponential risk operators to ensure robustness against model uncertainties. We introduce a distributed formulation of the safety filter by deriving two alternative strategies: one based on worst-case anticipation and another on proximity to a known safe policy. By allowing agents to switch between strategies, feasibility can be ensured. Through detailed numerical evaluations, we demonstrate the efficacy of our approach in maintaining safety without being overly conservative.