Multi-Objective Multi-Agent Path Finding with Lexicographic Cost Preferences

Many real-world scenarios require multiple agents to coordinate in shared environments, while balancing trade-offs between multiple, potentially competing objectives. Current multi-objective multi-agent path finding (MO-MAPF) algorithms typically produce conflict-free plans by computing Pareto frontiers. They do not explicitly optimize for user-defined preferences, even when the preferences are available, and scale poorly with the number of objectives. We propose a lexicographic framework for modeling MO-MAPF, along with an algorithm \textit{Lexicographic Conflict-Based Search} (LCBS) that directly computes a single solution aligned with a lexicographic preference over objectives. LCBS integrates a priority-aware low-level $A^*$ search with conflict-based search, avoiding Pareto frontier construction and enabling efficient planning guided by preference over objectives. We provide insights into optimality and scalability, and empirically demonstrate that LCBS computes optimal solutions while scaling to instances with up to ten objectives -- far beyond the limits of existing MO-MAPF methods. Evaluations on standard and randomized MAPF benchmarks show consistently higher success rates against state-of-the-art baselines, especially with increasing number of objectives.

Mitigating Negative Side Effects in Multi-Agent Systems Using Blame Assignment

When agents that are independently trained (or designed) to complete their individual tasks are deployed in a shared environment, their joint actions may produce negative side effects (NSEs). As their training does not account for the behavior of other agents or their joint action effects on the environment, the agents have no prior knowledge of the NSEs of their actions. We model the problem of mitigating NSEs in a cooperative multi-agent system as a Lexicographic Decentralized Markov Decision Process with two objectives. The agents must optimize the completion of their assigned tasks while mitigating NSEs. We assume independence of transitions and rewards with respect to the agents' tasks but the joint NSE penalty creates a form of dependence in this setting. To improve scalability, the joint NSE penalty is decomposed into individual penalties for each agent using credit assignment, which facilitates decentralized policy computation. Our results in simulation on three domains demonstrate the effectiveness and scalability of our approach in mitigating NSEs by updating the policies of a subset of agents in the system.