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Evolutionary science provides evidence that diversity confers resilience.Yet, traditional multi-agent reinforcement learning techniques commonly enforcehomogeneity to increase training sample efficiency. When a system of learningagents is not constrained to homogeneous policies, individual agents maydevelop diverse behaviors, resulting in emergent complementarity that benefitsthe system. Despite this feat, there is a surprising lack of tools that measurebehavioral diversity in systems of learning agents. Such techniques would pavethe way towards understanding the impact of diversity in collective resilienceand performance. In this paper, we introduce System Neural Diversity (SND): ameasure of behavioral heterogeneity for multi-agent systems where agents havestochastic policies. %over a continuous state space. We discuss and prove itstheoretical properties, and compare it with alternate, state-of-the-artbehavioral diversity metrics used in cross-disciplinary domains. Throughsimulations of a variety of multi-agent tasks, we show how our metricconstitutes an important diagnostic tool to analyze latent properties ofbehavioral heterogeneity. By comparing SND with task reward in static tasks,where the problem does not change during training, we show that it is key tounderstanding the effectiveness of heterogeneous vs homogeneous agents. Indynamic tasks, where the problem is affected by repeated disturbances duringtraining, we show that heterogeneous agents are first able to learn specializedroles that allow them to cope with the disturbance, and then retain these roleswhen the disturbance is removed. SND allows a direct measurement of this latentresilience, while other proxies such as task performance (reward) fail to.

System Neural Diversity: Measuring Behavioral Heterogeneity in Multi-Agent Learning