Achieving Equilibrium Under Utility Heterogeneity: An Agent-Attention Framework for Multi-Agent Multi-Objective Reinforcement Learning

Multi-agent multi-objective systems (MAMOS) have emerged as powerful frameworks for modelling complex decision-making problems across various real-world domains, such as robotic exploration, autonomous traffic management, and sensor network optimisation. MAMOS enhances scalability and robustness through decentralised control and more accurately captures inherent trade-offs between conflicting objectives. In MAMOS, each agent uses utility functions that map return vectors to scalar values. Existing MAMOS optimisation methods face significant challenges in handling heterogeneous objective and utility function settings, where training non-stationarity is intensified due to private utility functions and the associated policies. In this paper, we first theoretically prove that direct access to, or structured modeling of, global utility functions is necessary to achieve the Bayesian Nash Equilibrium under decentralised execution constraints. To access the global utility functions while preserving the decentralised execution, we propose an Agent-Attention Multi-Agent Multi-Objective Reinforcement Learning (AA-MAMORL) framework. Our approach implicitly learns a joint belief over other agents’ utility functions and their associated policies during centralised training, effectively mapping global states and utilities to each agent's policy. During execution, each agent independently selects actions based on local observations and its private utility function to approximate a BNE, without relying on inter-agent communication. We evaluate our framework through extensive experiments in a custom-designed MAMO Particle environment and the standard MOMALand benchmark. The results demonstrate that accessibility to global preferences and our proposed AA-MAMORL significantly improves performance and consistently outperforms state-of-the-art methods.