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Focusing on multi-agent task allocation problems, our goal is to study the question: What kinds of objectives are best suited for heterogeneous teams? We first consider an instantaneous, non-spatial setting where the global reward is built by two generalized aggregation operators: an inner operator that maps the N agents’ effort allocations on individual tasks to a task score, and an outer operator that merges the M task scores into the global team reward. We prove that the curvature of these operators determines whether heterogeneity can increase reward, and that for broad reward families this collapses to a simple convexity test. Next, we study heterogeneity in multi-agent reinforcement learning (MARL) and introduce Heterogeneous Environment Design (HED), a gradient-based algorithm that optimizes the parameter space of underspecified MARL environments to find scenarios where heterogeneity is advantageous.

In this work, we employ diversity measurement and control paradigms to study the impact of behavioral heterogeneity in several facets of multi-agent reinforcement learning. Through experiments in team play and other cooperative tasks, we show the emergence of unbiased behavioral roles that improve team outcomes; how behavioral diversity synergizes with morphological diversity; how diverse agents are more effective at finding cooperative solutions in sparse reward settings; and how behaviorally heterogeneous teams learn and retain latent skills to overcome repeated disruptions.

In this paper, we introduce System Neural Diversity (SND): a measure of behavioral heterogeneity for multi-agent systems where agents have stochastic policies. We discuss and prove its theoretical properties, and compare it with alternate, state-of-the-art behavioral diversity metrics used in cross-disciplinary domains. Through simulations of a variety of multi-agent tasks, we show how our metric constitutes an important diagnostic tool to analyze latent properties of behavioral heterogeneity.