Multi-agent reinforcement learning (MARL) has made significant progress in recent years, but most algorithms still rely on a discrete-time Markov Decision Process (MDP) with fixed decision intervals. This formulation is often ill-suited for complex multi-agent dynamics, particularly in high-frequency or irregular time-interval settings, leading to degraded performance and motivating the development of continuous-time MARL (CT-MARL). Existing CT-MARL methods are mainly built on Hamilton-Jacobi-Bellman (HJB) equations. However, they rarely account for safety constraints such as collision penalties, since these introduce discontinuities that make HJB-based learning difficult. To address this challenge, we propose a continuous-time constrained MDP (CT-CMDP) formulation and a novel MARL framework that transforms discrete MDPs into CT-CMDPs via an epigraph-based reformulation. We then solve this by proposing a novel physics-informed neural network (PINN)-based actor-critic method that enables stable and efficient optimization in continuous time. We evaluate our approach on continuous-time safe multi-particle environments (MPE) and safe multi-agent MuJoCo benchmarks. Results demonstrate smoother value approximations, more stable training, and improved performance over safe MARL baselines, validating the effectiveness and robustness of our method.
Figures & tables
Figure 1: Overview of the proposed epigraph-based CT-MARL framework. The pipeline begins with data collection, where individual agent rollouts are aggregated into a centralized rollout XR for the training; the outer optimization computes optimal z∗ to balance discounted cumulative cost and safety constraints; the inner optimization corresponds to critic learning, where return networks Vψret(x) and constraint value networks Vϕcons(x) are optimized jointly with the optimal auxiliary state z∗ ; and actor learning leverages the advantage function to improve policies.
Figure 2: Overall results for adapted MPE environments.
Figure 3: Performance of constraints and cost over MPE settings.
Figure 4: Overall results for adapted multi-agent MuJoCo environments.
Figure 5: Ablation study of different loss terms in critic network over MPE.
Figure 6: Performance of constraints and cost over MuJoCo settings.
Figure 7: Weighted loss performance.
Figure 8: Performance with and without epigraph reformulation.
Figure 9: Sensitivity test of different z choices.
Multi-agent systems are widely used in safety-critical applications that require coordinated behavior under strict safety constraints. Existing approaches face a fundamental trade-off: learning-based methods achieve strong empirical performance but lack theoretical safety guarantees, while control-theoretic methods enforce safety but often lead to overly conservative and inefficient behaviors. We propose a hierarchical multi-agent reinforcement learning framework that enforces hard safety constraints under mild assumptions at low level via a constraint manifold, while enabling effective coordination through high-level policy learning. Our approach provides theoretical safety guarantees in the multi-agent setting and yields stationary learning dynamics, thereby enabling stable and efficient training. Empirically, our method achieves competitive performance while maintaining nearly perfect safety rates, and generalizes effectively to varying numbers of agents and obstacles.
Zihao Guo, Jianing Zhao, Ling Li +3
1King’s College London · University of California, Berkeley · 3The Alan Turing Institute
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.
Zijie Meng, Ziwei Li, Yufei Liu +5
Peking University · National Taiwan University · WHU +1
This paper presents a graph-based safe multi-agent reinforcement learning (MARL) framework for cooperative navigation with time-varying topology. To address the critical challenge of ensuring safety in environments with sensing constraints, a safety-decoupled mechanism is introduced through a Control Barrier-Like Function (CBLF) action screening layer. This mechanism bridges the gap between discrete LiDAR perception and continuous safety constraints, ensuring that physical safety constraints are strictly satisfied regardless of the learning progress. Building upon this safety foundation, a unified structural architecture is proposed, integrating a attention-based actor and a Graph Attention Network (GAT) centralized critic. The actor utilizes a value vector reconstruction mechanism that explicitly encodes relative geometric relations through a collaborative tracking error matrix, enabling scale-insensitive policy learning under time-varying communication topologies. Meanwhile, the GAT-based critic models evolving interaction structures for accurate global value estimation. The proposed framework is validated on real differential-drive robot platforms, and experimental results demonstrate superior stability and safety in dynamic scenarios with limited fields-of-view.
Xiao Sizhe, Dong Lijing, Bai Rui +1
School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing, China