Causal Identification in Multi-Task Demand Learning with Confounding

2026-02-10

AI Summary

This study addresses the challenge of causal price effect identification in multi-task demand learning—such as retail pricing—where historical prices are often endogenously correlated with unobserved task-level demand factors due to managerial or algorithmic decisions, thereby confounding conventional estimation methods. To overcome this, the paper proposes a Decision-Conditioned Masked Outcome Meta-Learning (DCMOML) framework that ensures causal identifiability by carefully designing the meta-learner’s information set and imposing price-adaptivity constraints. This approach achieves, for the first time, identifiability of causal parameters under few-shot, strongly confounded multi-task settings, surpassing the limitations of traditional pooled regression and standard meta-learning. It enables accurate estimation of task-specific causal price response functions, offering rigorous theoretical guarantees for data-driven causal pricing strategies.

Technology Category

• Machine Learning: Causal Learning
• Search and Optimization: Learning to Search
• Reasoning under Uncertainty: Causality

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

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.

Problem

• causal identification
• multi-task learning
• endogeneity
• demand learning
• confounding

Innovation

• causal identification
• multi-task learning
• endogeneity
• meta-learning
• demand estimation