Causal Multi-Task Demand Learning

TL;DR

This paper introduces a meta-learning framework for estimating causal demand functions across multiple retail pricing tasks with limited price variation, addressing endogeneity and confounding issues.

Contribution

It proposes a novel information design that identifies causal demand parameters despite confounding, using a carefully chosen subset of task observables and exogenous prices.

Findings

Improved demand response recovery over standard transfer-learning methods.

Validated on real and synthetic data with better accuracy.

Addresses endogeneity in multi-task demand estimation.

Abstract

We study a canonical multi-task demand-learning problem motivated by retail pricing, where a firm seeks to estimate heterogeneous linear price-response functions across multiple decision contexts. Each context is described by rich covariates but exhibits limited price variation, motivating transfer learning across tasks. A central challenge in leveraging cross-task transfer is endogeneity: prices may be arbitrarily correlated with unobserved task-level demand determinants across tasks. We propose a new meta-learning framework that identifies the conditional mean of task-specific causal demand parameters given a subset of task-specific observables despite such confounding, assuming that each task contains at least two distinct locally exogenous price points. This subset is carefully designed to include all of the prices to address cross-task confounding, while masking two demand outcomes that provide randomized supervision to address identifiability issues arising from the inclusion of all prices. We show that this information design is maximally uniformly valid, in that any refinement of the conditioning set that reveals withheld-outcome information is not guaranteed to identify the conditional mean causal target. We validate our method on real and synthetic data, demonstrating improved recovery of demand responses relative to standard transfer-learning baselines.