Explore Overlap Boundary: Causal Effect Bounds via Assignment Replay from Stochastic Algorithm under Structural Non-Overlap

Stochastic algorithms assign personalized treatments such as videos or contexts whose features and outcomes vary across users. We study the conditional treatment-averaged causal effect of the treatment feature (C-TACE), with treatments generated from a stochastic algorithm. Under structural non-overlap, this estimand is unidentified as the non-realized treatment feature is concealed. We derive replay-aware causal bounds on C-TACE under non-overlap. When propensities are not logged, repeated replays are applied to estimate the propensity together with the non-realized feature. We show that the boundaries are in the form of function roots and that the bound is sharp under conditions, and we construct boundary estimators at finite replay counts. Rigorous theory has been developed on its asymptotic coverage. We also develop a replay-budget allocation method to improve bound efficiency. The method is comprehensively evaluated on semi-synthetic KuaiRec data, providing an applicable solution to non-overlap problem on causal effect under a stochastic algorithm.