In marketing, optimizing subsidy allocation to maximize overall profits is of substantial economic importance. Prior research has employed treatment effect estimation techniques to identify subsidy-sensitive items and design corresponding allocation strategies. However, more accurate treatment effect estimations do not necessarily lead to better allocations, underscoring the critical influence of decision boundaries in decision-making. This paper argues that optimal allocation fundamentally depends on predicting the expected optimal subsidy, a challenge distinct from conventional treatment effect estimation or causal decision-making, which existing approaches fail to address. To fill this gap, we introduce a two-stage Counterfactual optimal subsidy Learning method with an Asymmetric reward (CoLA). In the first stage, we derive a coarse estimate of the expected subsidy threshold by exploiting order information and the conditional independence between expected and observed subsidies. In the second stage, we refine these estimates using an asymmetric loss function, leading to more robust predictions. Under practical budget constraints, we prioritize candidates based on their Sharpe ratios to determine the final subsidy allocation strategy. Experiments on three public datasets and an online A/B test show that our method achieves significant performance improvements, yielding the highest total profit and incremental leverage ratios.

Post-click conversion rate (CVR) prediction is a central task in recommender systems, yet selection bias creates a severe distributional gap between the clicked training samples and the entire inference space. To address selection bias, propensity-based methods such as inverse propensity scoring (IPS) and doubly robust (DR) have been adopted, which aim to estimate the unbiased learning objective from biased training samples. However, these approaches assume strictly positive propensities, implying every user-item pair has a nonzero probability of interaction. In practice, such positivity assumption maybe violated, for example, in food-delivery platforms, some restaurants located more than 10 kilometers away will be blocked for recommendation. In this study, we theoretically show that when such zero-propensity samples, termed extrapolation samples exist, both IPS and DR estimators become biased. To overcome this limitation, we propose ExtraDebias method, which enables debiased recommendation in both non-extrapolation and extrapolation samples. Specifically, we first train a propensity model to identify extrapolation samples with extremely small propensity estimates, then estimate their pseudo-label intervals, and derive an upper bound of the learning objective for extrapolation samples. By minimizing the derived upper bound, debiased learning on extrapolation samples is ensured, while unbiased learning on non-extrapolation samples is achieved by standard IPS. Experiments on four real-world offline datasets and one online A/B test show that ExtraDebias effectively minimizes prediction errors on extrapolation samples and achieves optimal performance.