Pre-Trained AI Model Assisted Online Decision-Making under Missing Covariates: A Theoretical Perspective
This work addresses the challenge of integrating pre-trained models into decision-making processes for data-driven applications, offering theoretical insights that could enhance performance in domains with missing data.
The paper tackles the problem of sequential contextual decision-making with missing covariates by using a pre-trained AI model for imputation, introducing 'model elasticity' to quantify regret due to imputation errors and showing that calibration under missing at random settings improves regret guarantees.
We study a sequential contextual decision-making problem in which certain covariates are missing but can be imputed using a pre-trained AI model. From a theoretical perspective, we analyze how the presence of such a model influences the regret of the decision-making process. We introduce a novel notion called "model elasticity", which quantifies the sensitivity of the reward function to the discrepancy between the true covariate and its imputed counterpart. This concept provides a unified way to characterize the regret incurred due to model imputation, regardless of the underlying missingness mechanism. More surprisingly, we show that under the missing at random (MAR) setting, it is possible to sequentially calibrate the pre-trained model using tools from orthogonal statistical learning and doubly robust regression. This calibration significantly improves the quality of the imputed covariates, leading to much better regret guarantees. Our analysis highlights the practical value of having an accurate pre-trained model in sequential decision-making tasks and suggests that model elasticity may serve as a fundamental metric for understanding and improving the integration of pre-trained models in a wide range of data-driven decision-making problems.