We study a canonical multi-task demand learning problem motivated by retail pricing, in which a firm seeks to estimate heterogeneous linear price-response functions across a large collection of decision contexts. Each context is characterized by rich observable covariates yet typically exhibits only limited historical price variation, motivating the use of multi-task learning to borrow strength across tasks. A central challenge in this setting is endogeneity: historical prices are chosen by managers or algorithms and may be arbitrarily correlated with unobserved, task-level demand determinants. Under such confounding by latent fundamentals, commonly used approaches, such as pooled regression and meta-learning, fail to identify causal price effects. We propose a new estimation framework that achieves causal identification despite arbitrary dependence between prices and latent task structure. Our approach, Decision-Conditioned Masked-Outcome Meta-Learning (DCMOML), involves carefully designing the information set of a meta-learner to leverage cross-task heterogeneity while accounting for endogenous decision histories. Under a mild restriction on price adaptivity in each task, we establish that this method identifies the conditional mean of the task-specific causal parameters given the designed information set. Our results provide guarantees for large-scale demand estimation with endogenous prices and small per-task samples, offering a principled foundation for deploying causal, data-driven pricing models in operational environments.

翻译：本研究探讨了一个源于零售定价的典型多任务需求学习问题，其中企业需要估计大量决策情境下的异质性线性价格响应函数。每个情境均具有丰富的可观测协变量特征，但通常仅表现出有限的历史价格变异，这促使我们采用多任务学习方法以跨任务共享信息。该场景的核心挑战在于内生性：历史价格由管理者或算法设定，可能与未观测到的任务层面需求决定因素存在任意相关性。在此类潜在基本面混杂的情况下，常用方法（如池化回归和元学习）无法识别因果价格效应。我们提出了一种新的估计框架，即使在价格与潜在任务结构存在任意依赖关系时仍能实现因果识别。我们的方法——决策条件掩码结果元学习（DCMOML）——通过精心设计元学习器的信息集，在考虑内生决策历史的同时利用跨任务异质性。在对每个任务的价格适应性施加温和限制的条件下，我们证明该方法能够识别给定设计信息集的任务特定因果参数的条件期望。我们的研究结果为具有内生价格和小样本任务的大规模需求估计提供了理论保证，为在运营环境中部署因果驱动的数据驱动定价模型奠定了理论基础。