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

arXiv: https://arxiv.org/abs/2507.07852 · HTML: https://mlsanity.com/paper/2507.07852/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 63 references that are in the map.
- First posted on arXiv 10 Jul 2025.

## Builds on (most cited first, 30 of 33)

- [CheXpert: A Large Chest Radiograph Dataset with Uncertainty Labels and Expert Comparison](https://mlsanity.com/paper/1901.07031/) (2019)
- [Meta Pseudo Labels](https://mlsanity.com/paper/2003.10580/) (2020)
- [Beyond UCB: Optimal and Efficient Contextual Bandits with Regression Oracles](https://mlsanity.com/paper/2002.04926/) (2020)
- [Does Synthetic Data Generation of LLMs Help Clinical Text Mining?](https://mlsanity.com/paper/2303.04360/) (2023)
- [Bypassing the Monster: A Faster and Simpler Optimal Algorithm for Contextual Bandits under Realizability](https://mlsanity.com/paper/2003.12699/) (2020)
- [Adapting to Misspecification in Contextual Bandits](https://mlsanity.com/paper/2107.05745/) (2021)
- [Synthetic Data Generation Using Large Language Models: Advances in Text and Code](https://mlsanity.com/paper/2503.14023/) (2025)
- [Misspecified Gaussian Process Bandit Optimization](https://mlsanity.com/paper/2111.05008/) (2021)
- [Data Augmentation for Intent Classification with Off-the-shelf Large Language Models](https://mlsanity.com/paper/2204.01959/) (2022)
- [Efficient and Optimal Algorithms for Contextual Dueling Bandits under Realizability](https://mlsanity.com/paper/2111.12306/) (2021)
- [Double/Debiased Machine Learning for Treatment and Causal Parameters](https://mlsanity.com/paper/1608.00060/) (2016)
- [LOLA: LLM-Assisted Online Learning Algorithm for Content Experiments](https://mlsanity.com/paper/2406.02611/) (2024)
- [Automatic Debiased Machine Learning for Covariate Shifts](https://mlsanity.com/paper/2307.04527/) (2023)
- [Collaborative Prediction: Tractable Information Aggregation via Agreement](https://mlsanity.com/paper/2504.06075/) (2025)
- [Offline Contextual Multi-armed Bandits for Mobile Health Interventions: A Case Study on Emotion Regulation](https://mlsanity.com/paper/2008.09472/) (2020)
- [Tractable Agreement Protocols](https://mlsanity.com/paper/2411.19791/) (2024)
- [Optimal Contextual Bandits with Knapsacks under Realizability via Regression Oracles](https://mlsanity.com/paper/2210.11834/) (2022)
- [Semi-Supervised Semantic Segmentation Based on Pseudo-Labels: A Survey](https://mlsanity.com/paper/2403.01909/) (2024)
- [On Dynamic Pricing with Covariates](https://mlsanity.com/paper/2112.13254/) (2021)
- [Active Exploration via Autoregressive Generation of Missing Data](https://mlsanity.com/paper/2405.19466/) (2024)
- [Contextual User Browsing Bandits for Large-Scale Online Mobile Recommendation](https://mlsanity.com/paper/2008.09368/) (2020)
- [Offline Oracle-Efficient Learning for Contextual MDPs via Layerwise Exploration-Exploitation Tradeoff](https://mlsanity.com/paper/2405.17796/) (2024)
- [The Application of Large Language Models in Recommendation Systems](https://mlsanity.com/paper/2501.02178/) (2025)
- [Statistically Valid Post-Deployment Monitoring Should Be Standard for AI-Based Digital Health](https://mlsanity.com/paper/2506.05701/) (2025)
- [Contextual Bandit with Missing Rewards](https://mlsanity.com/paper/2007.06368/) (2020)
- [Contextual Thompson Sampling via Generation of Missing Data](https://mlsanity.com/paper/2502.07064/) (2025)
- [Contextual Online Decision Making with Infinite-Dimensional Functional Regression](https://mlsanity.com/paper/2501.18359/) (2025)
- [LLM aided semi-supervision for Extractive Dialog Summarization](https://mlsanity.com/paper/2311.11462/) (2023)
- [Dynamic Pricing in the Linear Valuation Model using Shape Constraints](https://mlsanity.com/paper/2502.05776/) (2025)
- [Linear Bandits with Partially Observable Features](https://mlsanity.com/paper/2502.06142/) (2025)

## Built on by (most cited first, 3 of 3)

- [LLM-Inspired Pretrain-Then-Finetune for Small-Data, Large-Scale Optimization](https://mlsanity.com/paper/2602.03690/) (2026)
- [Perturbing the Derivative: Wild Refitting for Model-Free Evaluation of Machine Learning Models under Bregman Losses](https://mlsanity.com/paper/2509.02476/) (2025)
- [Learning with Incomplete Context: Linear Contextual Bandits with Pretrained Imputation](https://mlsanity.com/paper/2510.09908/) (2025)

## Abstract (arXiv)

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.