Graph Neural Network-based Resource AllocationStrategies for Multi-Object Spectroscopy

Resource allocation problems are often approached with linear program-ming techniques. But many concrete allocation problems in the experimental and ob-servational sciences cannot or should not be expressed in the form of linear objectivefunctions. Even if the objective is linear, its parameters may not be known beforehandbecause they depend on the results of the experiment for which the allocation is to bedetermined. To address these challenges, we present a bipartite Graph Neural Networkarchitecture for trainable resource allocation strategies. Items of value and constraintsform the two sets of graph nodes, which are connected by edges corresponding to pos-sible allocations. The GNN is trained on simulations or past problem occurrences tomaximize any user-supplied, scientifically motivated objective function, augmented byan infeasibility penalty. The amount of feasibility violation can be tuned in relation toany available slack in the system. We apply this method to optimize the astronomicaltarget selection strategy for the highly multiplexed Subaru Prime Focus Spectrographinstrument, where it shows superior results to direct gradient descent optimization andextends the capabilities of the currently employed solver which uses linear objectivefunctions. The development of this method enables fast adjustment and deployment ofallocation strategies, statistical analyses of allocation patterns, and fully differentiable,science-driven solutions for resource allocation problems.