CASI: Credit Assignment via Set Intervention for Agentic Retrieval

Large language models increasingly generate multiple retrieval actions jointly, while downstream systems often provide only one reward for the resulting set. Broadcasting this reward provides a valid score-function gradient estimator for the expected set-level objective, but does not determine a coalition-dependent within-set attribution. We introduce **CASI (Credit Assignment via Set Intervention)**, which constructs the missing counterfactual information through snapshot-grounded set intervention: generate and retrieve once, hold replayable snapshot components fixed, and evaluate alternative subsets under common conditions. Shapley aggregation converts these marginals into within-set credit, which bounded zero-sum advantage shaping incorporates into policy optimization. For \(m \ge 4\), singleton, leave-one-out, and full-set endpoints do not generally determine the Shapley allocation; under additive set values, extra coalition evaluations are redundant. In a five-action sponsored-search setting, exhaustive auction replay over 1,200 requests reveals substantial coalition dependence. Under the training-time evaluator, CASI achieves the highest median cosine similarity to a replay-defined Shapley reference among evaluated credit rules; under a sensitivity backend, CASI does not outperform Singleton. Across five independent training runs, CASI-trained policies achieve higher held-out auction-replay set value than Singleton- or Broadcast-trained policies. In a randomized seven-day production A/B test on 10% of traffic, the CASI-trained policy yields an observed **3.51%** lift in the primary advertiser-value metric over production control.