# RoMFAC: A robust mean-field actor-critic reinforcement learning against adversarial perturbations on states

arXiv: https://arxiv.org/abs/2205.07229 · HTML: https://mlsanity.com/paper/2205.07229/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 62 references that are in the map.
- First posted on arXiv 15 May 2022.

## Builds on (most cited first, 26 of 26)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Multi-Agent Actor-Critic for Mixed Cooperative-Competitive Environments](https://mlsanity.com/paper/1706.02275/) (2017)
- [The Surprising Effectiveness of PPO in Cooperative, Multi-Agent Games](https://mlsanity.com/paper/2103.01955/) (2021)
- [QMIX: Monotonic Value Function Factorisation for Deep Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/1803.11485/) (2018)
- [Monotonic Value Function Factorisation for Deep Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2003.08839/) (2020)
- [Sim-to-Real Transfer in Deep Reinforcement Learning for Robotics: a Survey](https://mlsanity.com/paper/2009.13303/) (2020)
- [On the Effectiveness of Interval Bound Propagation for Training Verifiably Robust Models](https://mlsanity.com/paper/1810.12715/) (2018)
- [Adversarial Attacks on Neural Network Policies](https://mlsanity.com/paper/1702.02284/) (2017)
- [QPLEX: Duplex Dueling Multi-Agent Q-Learning](https://mlsanity.com/paper/2008.01062/) (2020)
- [Actor-Attention-Critic for Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/1810.02912/) (2018)
- [Robust Deep Reinforcement Learning against Adversarial Perturbations on State Observations](https://mlsanity.com/paper/2003.08938/) (2020)
- [Mean Field Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/1802.05438/) (2018)
- [Robust Reinforcement Learning on State Observations with Learned Optimal Adversary](https://mlsanity.com/paper/2101.08452/) (2021)
- [A Comprehensive Survey of Scene Graphs: Generation and Application](https://mlsanity.com/paper/2104.01111/) (2021)
- [Wasserstein Adversarial Examples via Projected Sinkhorn Iterations](https://mlsanity.com/paper/1902.07906/) (2019)
- [Robust Deep Reinforcement Learning through Adversarial Loss](https://mlsanity.com/paper/2008.01976/) (2020)
- [MAgent: A Many-Agent Reinforcement Learning Platform for Artificial Collective Intelligence](https://mlsanity.com/paper/1712.00600/) (2017)
- [Stealthy and Efficient Adversarial Attacks against Deep Reinforcement Learning](https://mlsanity.com/paper/2005.07099/) (2020)
- [Challenges and Countermeasures for Adversarial Attacks on Deep Reinforcement Learning](https://mlsanity.com/paper/2001.09684/) (2020)
- [On the Robustness of Cooperative Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2003.03722/) (2020)
- [Stop-and-Go: Exploring Backdoor Attacks on Deep Reinforcement Learning-based Traffic Congestion Control Systems](https://mlsanity.com/paper/2003.07859/) (2020)
- [Q-value Path Decomposition for Deep Multiagent Reinforcement Learning](https://mlsanity.com/paper/2002.03950/) (2020)
- [ROMAX: Certifiably Robust Deep Multiagent Reinforcement Learning via Convex Relaxation](https://mlsanity.com/paper/2109.06795/) (2021)
- [Transferring Multi-Agent Reinforcement Learning Policies for Autonomous Driving using Sim-to-Real](https://mlsanity.com/paper/2203.11653/) (2022)
- [Sim-to-Real Transfer of Accurate Grasping with Eye-In-Hand Observations and Continuous Control](https://mlsanity.com/paper/1712.03303/) (2017)

## Built on by (most cited first, 16 of 16)

- [Robust Multi-Agent Reinforcement Learning via Adversarial Regularization: Theoretical Foundation and Stable Algorithms](https://mlsanity.com/paper/2310.10810/) (2023)
- [Asynchronous Distributed Bilevel Optimization](https://mlsanity.com/paper/2212.10048/) (2022)
- [Safe Reinforcement Learning with Dual Robustness](https://mlsanity.com/paper/2309.06835/) (2023)
- [Partially Observable Mean Field Multi-Agent Reinforcement Learning Based on Graph-Attention](https://mlsanity.com/paper/2304.12653/) (2023)
- [Robustness Testing for Multi-Agent Reinforcement Learning: State Perturbations on Critical Agents](https://mlsanity.com/paper/2306.06136/) (2023)
- [Wolfpack Adversarial Attack for Robust Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2502.02844/) (2025)
- [Multi-Agent Reinforcement Learning: Methods, Applications, Visionary Prospects, and Challenges](https://mlsanity.com/paper/2305.10091/) (2023)
- [Enhancing the Robustness of QMIX against State-adversarial Attacks](https://mlsanity.com/paper/2307.00907/) (2023)
- [Security of Deep Reinforcement Learning for Autonomous Driving: A Survey](https://mlsanity.com/paper/2212.06123/) (2022)
- [PNAct: Crafting Backdoor Attacks in Safe Reinforcement Learning](https://mlsanity.com/paper/2507.00485/) (2025)
- [Robust and Efficient Communication in Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2511.11393/) (2025)
- [Rollout Total Correlation for Deep Reinforcement Learning](https://mlsanity.com/paper/2209.05333/) (2022)
- [Off-OAB: Off-Policy Policy Gradient Method with Optimal Action-Dependent Baseline](https://mlsanity.com/paper/2405.02572/) (2024)
- [Policy Disruption in Reinforcement Learning:Adversarial Attack with Large Language Models and Critical State Identification](https://mlsanity.com/paper/2507.18113/) (2025)
- [Pruning Cannot Hurt Robustness: Certified Trade-offs in Reinforcement Learning](https://mlsanity.com/paper/2510.12939/) (2025)
- [Diffusion Policy with Behavioral Advantage Correction for Offline Reinforcement Learning](https://mlsanity.com/paper/2608.02332/) (2026)

## Abstract (arXiv)

Multi-agent deep reinforcement learning makes optimal decisions dependent on system states observed by agents, but any uncertainty on the observations may mislead agents to take wrong actions. The Mean-Field Actor-Critic reinforcement learning (MFAC) is well-known in the multi-agent field since it can effectively handle a scalability problem. However, it is sensitive to state perturbations that can significantly degrade the team rewards. This work proposes a Robust Mean-field Actor-Critic reinforcement learning (RoMFAC) that has two innovations: 1) a new objective function of training actors, composed of a policy gradient function that is related to the expected cumulative discount reward on sampled clean states and an action loss function that represents the difference between actions taken on clean and adversarial states; and 2) a repetitive regularization of the action loss, ensuring the trained actors to obtain excellent performance. Furthermore, this work proposes a game model named a State-Adversarial Stochastic Game (SASG). Despite the Nash equilibrium of SASG may not exist, adversarial perturbations to states in the RoMFAC are proven to be defensible based on SASG. Experimental results show that RoMFAC is robust against adversarial perturbations while maintaining its competitive performance in environments without perturbations.