# TRIDENT: Breaking the Hybrid-Safety-Physics Coupling for Provably Safe Multi-Agent Reinforcement Learning

arXiv: https://arxiv.org/abs/2606.18308 · HTML: https://mlsanity.com/paper/2606.18308/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 42 references that are in the map.
- First posted on arXiv 16 Jun 2026.

## Builds on (most cited first, 25 of 25)

- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Multi-Agent Actor-Critic for Mixed Cooperative-Competitive Environments](https://mlsanity.com/paper/1706.02275/) (2017)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Constrained Policy Optimization](https://mlsanity.com/paper/1705.10528/) (2017)
- [The Surprising Effectiveness of PPO in Cooperative, Multi-Agent Games](https://mlsanity.com/paper/2103.01955/) (2021)
- [The StarCraft Multi-Agent Challenge](https://mlsanity.com/paper/1902.04043/) (2019)
- [Safe Reinforcement Learning via Shielding](https://mlsanity.com/paper/1708.08611/) (2017)
- [Responsive Safety in Reinforcement Learning by PID Lagrangian Methods](https://mlsanity.com/paper/2007.03964/) (2020)
- [A Lyapunov-based Approach to Safe Reinforcement Learning](https://mlsanity.com/paper/1805.07708/) (2018)
- [Residual Reinforcement Learning for Robot Control](https://mlsanity.com/paper/1812.03201/) (2018)
- [FACMAC: Factored Multi-Agent Centralised Policy Gradients](https://mlsanity.com/paper/2003.06709/) (2020)
- [Residual Policy Learning](https://mlsanity.com/paper/1812.06298/) (2018)
- [Global Convergence of Multi-Agent Policy Gradient in Markov Potential Games](https://mlsanity.com/paper/2106.01969/) (2021)
- [Safe Multi-Agent Reinforcement Learning via Shielding](https://mlsanity.com/paper/2101.11196/) (2021)
- [Hybrid Actor-Critic Reinforcement Learning in Parameterized Action Space](https://mlsanity.com/paper/1903.01344/) (2019)
- [Reducing Overestimation Bias in Multi-Agent Domains Using Double Centralized Critics](https://mlsanity.com/paper/1910.01465/) (2019)
- [Rao-Blackwellizing the Straight-Through Gumbel-Softmax Gradient Estimator](https://mlsanity.com/paper/2010.04838/) (2020)
- [Multi-Agent Constrained Policy Optimisation](https://mlsanity.com/paper/2110.02793/) (2021)
- [Deep Multi-Agent Reinforcement Learning with Discrete-Continuous Hybrid Action Spaces](https://mlsanity.com/paper/1903.04959/) (2019)
- [Safe reinforcement learning for probabilistic reachability and safety specifications: A Lyapunov-based approach](https://mlsanity.com/paper/2002.10126/) (2020)
- [Physics-Regulated Deep Reinforcement Learning: Invariant Embeddings](https://mlsanity.com/paper/2305.16614/) (2023)
- [SynPo: Boosting Training-Free Few-Shot Medical Segmentation via High-Quality Negative Prompts](https://mlsanity.com/paper/2506.15153/) (2025)
- [ARGUS: Stacked Multi-View Identity Mosaic Injection for Subject-Preserving Video Generation](https://mlsanity.com/paper/2606.11670/) (2026)
- [Safe Multi-Agent Reinforcement Learning with Convergence to Generalized Nash Equilibrium](https://mlsanity.com/paper/2411.15036/) (2024)
- [Decoupling Semantics from Distortions: Multi-Scale Two-Stream Vision-Language Alignment for AI-Generated Image Quality Assessment](https://mlsanity.com/paper/2606.16799/) (2026)

## Built on by (most cited first, 2 of 2)

- [ParaScale: Scale-Calibrated Camera-Motion Transfer via a Gauge-Invariant Parallax Number](https://mlsanity.com/paper/2606.19805/) (2026)
- [OrthoMotion:Disentangling Camera and Subject Motion via Geometry Semantics Orthogonal Attention](https://mlsanity.com/paper/2606.22835/) (2026)

## Abstract (arXiv)

Safe coordination in networked cyber-physical systems forces learning algorithms to simultaneously handle hybrid discrete-continuous actions, hard training-time safety constraints, and physics-governed dynamics. We show that these three features form a directed cycle of biases that defeats any naive composition of off-the-shelf modules, and formalize this as a three-way coupling lemma. We then introduce TRIDENT, the first MARL framework whose three components are co-designed to cancel each leak: a Richardson-Romberg gradient correction reducing Gumbel-Softmax bias from O(tau) to O(tau^2), a Lyapunov-constrained sequential trust-region update enforcing per-iterate feasibility, and a physics-informed residual critic that decomposes value rather than reward. We prove an O~(1/sqrt(K)) convergence rate to a constrained Nash equilibrium and an O(sqrt(K)) cumulative-violation bound. On multi-UAV mobile-edge computing, autonomous intersection management, and a hybrid SMAC variant, TRIDENT cuts training-time violations by 95.5% over MADDPG and 76.3% over MACPO, while improving reward by 13.5% over the strongest unconstrained baseline.