Coordinating agents to complete a set of tasks with intercoupled temporal and resource constraints is computationally challenging, yet human domain experts can solve these difficult scheduling problems using paradigms learned through years of apprenticeship. A process for manually codifying this domain knowledge within a computational framework is necessary to scale beyond the "single-expert, single-trainee" apprenticeship model. However, human domain experts often have difficulty describing their decision-making processes. We propose a new approach for capturing this decision-making process through counterfactual reasoning in pairwise comparisons. Our approach is model-free and does not require iterating through the state space. We demonstrate that this approach accurately learns multifaceted heuristics on a synthetic and real world data sets. We also demonstrate that policies learned from human scheduling demonstration via apprenticeship learning can substantially improve the efficiency of schedule optimization. We employ this human-machine collaborative optimization technique on a variant of the weapon-to-target assignment problem. We demonstrate that this technique generates optimal solutions up to 9.5 times faster than a state-of-the-art optimization algorithm.
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