Pre-Trained AI Model Assisted Online Decision-Making under Missing Covariates: A Theoretical Perspective

TL;DR

This paper provides a theoretical analysis of how pre-trained AI models influence regret in online decision-making with missing covariates, introducing the concept of model elasticity and showing calibration methods to improve performance.

Contribution

It introduces the novel concept of model elasticity to quantify regret due to imputation errors and demonstrates calibration techniques to enhance decision-making under missing data.

Findings

Model elasticity characterizes regret due to imputation discrepancy.

Calibration using orthogonal statistical learning improves imputation quality.

Accurate pre-trained models significantly reduce regret in decision tasks.

Abstract

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.