Causal Identification in Multi-Task Demand Learning with Confounding
Varun Gupta, Vijay Kamble
TL;DR
This paper tackles causal identification in multi-task demand learning when historical prices are endogenously set and potentially correlated with unobserved demand determinants. It shows that standard pooled or meta-learning approaches can converge to policy-dependent estimands and may fail to identify true causal price effects. The authors propose Decision-Conditioned Masked-Outcome Meta-Learning (DCMOML), an information-design framework that conditions on the price path to absorb latent confounding while masking two candidate query outcomes to prevent identifiability collapse; under a mild exogeneity condition on the final two-price block, DCMOML identifies the conditional mean of task-specific causal parameters and is statistically consistent. Empirically, DCMOML outperforms baselines in synthetic experiments with varying confounding and on real UK online-retail data, showing practical gains in large-scale pricing settings where randomized experiments are infeasible. The work bridges demand estimation under endogeneity with cross-task transfer and provides a scalable, identification-based approach for causal pricing in operational environments.
Abstract
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.