Action-Centered Causal Bandits for Budget-Constrained Promotion Targeting

Yifan Lin, Kaixu Yang, Di Mo

Web platforms select among costly interventions for each user to maximize incremental outcomes under a global budget. We formulate this problem as a budget-constrained contextual bandit with heterogeneous treatment effects. Although an action-independent outcome baseline cancels from treatment comparisons, modeling a nonlinear baseline can increase statistical complexity. We propose DR-CATE-CBwK, an action-centered causal bandit that directly learns treatment contrasts. Its online update remains valid under baseline-model misspecification without inverse-propensity weighting. It combines an offline doubly robust learner to warm-start treatment-effect estimates, an online action-centered estimator for sequential contrast learning, and a primal-dual controller with an affordable-action rule to enforce the effective-cost budget pathwise. For linear conditional average treatment effects (CATEs) in a stationary i.i.d. setting, we prove a high-probability (\widetilde{O}(Kd\sqrt{T})) regret bound, where K is the number of priced actions, d the context dimension, and T the horizon. We benchmark against the fluid linear program (LP) under the coverage-guaranteed action rule. We further…