CACTI: Cross-Action Counterfactual Transition Inference from Offline Data

Same-event counterfactual transition inference asks what the next state would have been under a different action while keeping the disturbance realized in the observed event fixed. Accurately fitting action-conditional transition distributions alone does not determine these same-event pairings, especially under uneven action coverage. We propose CACTI, a structured transition causal model that combines a shared state-dependent action response with a conditional invertible model of event-specific variation. This structure lets variation across related actions constrain queries with little direct data while retaining information from the factual event. Under a linear shared-response model and sequential exogeneity, we prove that, at a fixed state and without additional cross-state restrictions, the response to a query action difference is identifiable if and only if that direction lies in the range of the conditional action covariance. We further derive a local counterfactual error bound in terms of shared-response mismatch and action distance. We evaluate CACTI against same-event simulator oracles on four control tasks. It achieves the lowest mean counterfactual error on both all nonfactual queries and low-direct-support subsets, outperforming the compared predictive and explicit-abduction baselines. Policy-learning experiments with limited data further show that the generated counterfactual transitions can provide useful signals for downstream training.