CAPO: Counterfactual Credit Assignment in Sequential Cooperative Teams

Abstract: In cooperative teams where agents act in a fixed order and share a single team reward, it is hard to know how much each agent contributed, and harder still when agents are updated one at a time because data collected earlier no longer reflects the new policies. We introduce the Sequential Aristocrat Utility (SeqAU), the unique per-agent learning signal that maximizes the individual learnability of each agent's action, extending the classical framework of Wolpert and Tumer (2002) to this sequential setting. From SeqAU we derive CAPO (Counterfactual Advantage Policy Optimization), a critic-free policy-gradient algorithm. CAPO fits a per-agent reward decomposition from group rewards and computes the per-agent advantage in closed form plus a handful of forward passes through the current policy, requiring no extra environment calls beyond the initial batch. We give analytic bias and variance bounds and validate them on a controlled sequential bandit, where CAPO's advantage over standard baselines grows with the team size. The framework is general; multi-LLM pipelines are a natural deployment target.