# Safe Policy Synthesis in Multi-Agent POMDPs via Discrete-Time Barrier Functions

arXiv: https://arxiv.org/abs/1903.07823 · HTML: https://mlsanity.com/paper/1903.07823/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Mar 2019.

## Built on by (most cited first, 11 of 11)

- [Partially Observable Markov Decision Processes in Robotics: A Survey](https://mlsanity.com/paper/2209.10342/) (2022)
- [Generalizing Safety Beyond Collision-Avoidance via Latent-Space Reachability Analysis](https://mlsanity.com/paper/2502.00935/) (2025)
- [CBF-RL: Safety Filtering Reinforcement Learning in Training with Control Barrier Functions](https://mlsanity.com/paper/2510.14959/) (2025)
- [Trajectory Generation, Control, and Safety with Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2306.15512/) (2023)
- [Online Control Barrier Functions for Decentralized Multi-Agent Navigation](https://mlsanity.com/paper/2303.04313/) (2023)
- [Discrete GCBF Proximal Policy Optimization for Multi-agent Safe Optimal Control](https://mlsanity.com/paper/2502.03640/) (2025)
- [Safe Beyond the Horizon: Efficient Sampling-based MPC with Neural Control Barrier Functions](https://mlsanity.com/paper/2502.15006/) (2025)
- [Barrier Certificates for Unknown Systems with Latent States and Polynomial Dynamics using Bayesian Inference](https://mlsanity.com/paper/2504.01807/) (2025)
- [Distributed Risk-Sensitive Safety Filters for Uncertain Discrete-Time Systems](https://mlsanity.com/paper/2506.07347/) (2025)
- [Sample Efficient Certification of Discrete-Time Control Barrier Functions](https://mlsanity.com/paper/2509.03899/) (2025)
- [D-SafeMPC: Diffusion-Driven Safe Model Predictive Control with Discrete-Time Control Barrier Functions](https://mlsanity.com/paper/2607.10842/) (2026)

## Abstract (arXiv)

A multi-agent partially observable Markov decision process (MPOMDP) is a modeling paradigm used for high-level planning of heterogeneous autonomous agents subject to uncertainty and partial observation. Despite their modeling efficiency, MPOMDPs have not received significant attention in safety-critical settings. In this paper, we use barrier functions to design policies for MPOMDPs that ensure safety. Notably, our method does not rely on discretization of the belief space, or finite memory. To this end, we formulate sufficient and necessary conditions for the safety of a given set based on discrete-time barrier functions (DTBFs) and we demonstrate that our formulation also allows for Boolean compositions of DTBFs for representing more complicated safe sets. We show that the proposed method can be implemented online by a sequence of one-step greedy algorithms as a standalone safe controller or as a safety-filter given a nominal planning policy. We illustrate the efficiency of the proposed methodology based on DTBFs using a high-fidelity simulation of heterogeneous robots.