# Regret Minimization and Statistical Inference in Online Decision Making with High-dimensional Covariates

arXiv: https://arxiv.org/abs/2411.06329 · HTML: https://mlsanity.com/paper/2411.06329/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Nov 2024.

## Built on by (most cited first, 5 of 5)

- [Online Experimental Design With Estimation-Regret Trade-off Under Network Interference](https://mlsanity.com/paper/2412.03727/) (2024)
- [Logging Policy Design for Off-Policy Evaluation](https://mlsanity.com/paper/2605.15108/) (2026)
- [Design-Based Bandits Under Network Interference: Trade-Off Between Regret and Statistical Inference](https://mlsanity.com/paper/2510.07646/) (2025)
- [Beyond ATE: Multi-Criteria Design for A/B Testing](https://mlsanity.com/paper/2509.05864/) (2025)
- [Adaptive Inference for Resource-Constrained Dynamic Pricing](https://mlsanity.com/paper/2606.03736/) (2026)

## Abstract (arXiv)

This paper investigates regret minimization, statistical inference, and their interplay in high-dimensional online decision-making based on the sparse linear context bandit model. We integrate the varepsilon-greedy bandit algorithm for decision-making with a hard thresholding algorithm for estimating sparse bandit parameters and introduce an inference framework based on a debiasing method using inverse propensity weighting. Under a margin condition, our method achieves either O(T1/2) regret or classical O(T1/2)-consistent inference, indicating an unavoidable trade-off between exploration and exploitation. If a diverse covariate condition holds, we demonstrate that a pure-greedy bandit algorithm, i.e., exploration-free, combined with a debiased estimator based on average weighting can simultaneously achieve optimal O(log T) regret and O(T1/2)-consistent inference. We also show that a simple sample mean estimator can provide valid inference for the optimal policy's value. Numerical simulations and experiments on Warfarin dosing data validate the effectiveness of our methods.