Estimation of heterogeneous long-term treatment effects (HLTEs) is widely used for personalized decision-making in marketing, economics, and medicine, where short-term randomized experiments are often combined with long-term observational data. However, HLTE estimation is challenging due to limited overlap in treatment or in observing long-term outcomes for certain subpopulations, which can lead to unstable HLTE estimates with large finite-sample variance. To address this challenge, we introduce the LT-O-learners (Long-Term Orthogonal Learners), a set of novel orthogonal learners for HLTE estimation. The learners are designed for the canonical HLTE setting that combines a short-term randomized dataset $\mathcal{D}_1$ with a long-term historical dataset $\mathcal{D}_2$. The key idea of our LT-O-Learners is to retarget the learning objective by introducing custom overlap weights that downweight samples with low overlap in treatment or in long-term observation. We show that the retargeted loss is equivalent to the weighted oracle loss and satisfies Neyman-orthogonality, which means our learners are robust to errors in the nuisance estimation. We further provide a general error bound for the LT-O-Learners and give the conditions under which quasi-oracle rate can be achieved. Finally, our LT-O-learners are model-agnostic and can thus be instantiated with arbitrary machine learning models. We conduct empirical evaluations on synthetic and semi-synthetic benchmarks to confirm the theoretical properties of our LT-O-Learners, especially the robustness in low-overlap settings. To the best of our knowledge, ours are the first orthogonal learners for HLTE estimation that are robust to low overlap that is common in long-term outcomes.

翻译：异质性长期处理效应（HLTE）估计广泛应用于市场营销、经济学和医学领域的个性化决策，常将短期随机实验与长期观测数据相结合。然而，由于特定子群体在处理分配或长期结果观测中存在有限重叠，HLTE估计面临挑战，可能导致估计量不稳定且有限样本方差较大。为解决该问题，我们提出LT-O-学习器（面向长期结果的正交学习器），这是一组用于HLTE估计的新型正交学习器。该学习器针对典型HLTE场景设计，结合短期随机数据集$\mathcal{D}_1$与长期历史数据集$\mathcal{D}_2$。其核心思想是通过引入自定义重叠权重重新定位学习目标，降低处理分配或长期观测中低重叠样本的权重。我们证明重新定位的损失函数等价于加权理想损失函数，并满足奈曼正交性，从而对干扰项估计误差具有鲁棒性。进一步地，我们给出了LT-O-学习器的通用误差界，并推导了达到准理想率所需的条件。该方法与模型无关，可基于任意机器学习模型实现。通过合成数据集与半合成基准实验，我们验证了LT-O-学习器的理论性质，特别是低重叠场景下的鲁棒性。据我们所知，这是首个针对HLTE估计中常见长期结果低重叠问题具有鲁棒性的正交学习器。