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Many real-world problems contain multiple objectives and agents, where atrade-off exists between objectives. Key to solving such problems is to exploitsparse dependency structures that exist between agents. For example, in windfarm control a trade-off exists between maximising power and minimising stresson the systems components. Dependencies between turbines arise due to the wakeeffect. We model such sparse dependencies between agents as a multi-objectivecoordination graph (MO-CoG). In multi-objective reinforcement learning autility function is typically used to model a users preferences overobjectives, which may be unknown a priori. In such settings a set of optimalpolicies must be computed. Which policies are optimal depends on whichoptimality criterion applies. If the utility function of a user is derived frommultiple executions of a policy, the scalarised expected returns (SER) must beoptimised. If the utility of a user is derived from a single execution of apolicy, the expected scalarised returns (ESR) criterion must be optimised. Forexample, wind farms are subjected to constraints and regulations that must beadhered to at all times, therefore the ESR criterion must be optimised. ForMO-CoGs, the state-of-the-art algorithms can only compute a set of optimalpolicies for the SER criterion, leaving the ESR criterion understudied. Tocompute a set of optimal polices under the ESR criterion, also known as the ESRset, distributions over the returns must be maintained. Therefore, to compute aset of optimal policies under the ESR criterion for MO-CoGs, we present a noveldistributional multi-objective variable elimination (DMOVE) algorithm. Weevaluate DMOVE in realistic wind farm simulations. Given the returns inreal-world wind farm settings are continuous, we utilise a model known asreal-NVP to learn the continuous return distributions to calculate the ESR set.

Multi-Objective Coordination Graphs for the Expected Scalarised Returns with Generative Flow Models