# Robustly Improving Bandit Algorithms with Confounded and Selection Biased Offline Data: A Causal Approach

arXiv: https://arxiv.org/abs/2312.12731 · HTML: https://mlsanity.com/paper/2312.12731/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 31 references that are in the map.
- First posted on arXiv 20 Dec 2023.

## Builds on (most cited first, 4 of 4)

- [Adaptive Exploration in Linear Contextual Bandit](https://mlsanity.com/paper/1910.06996/) (2019)
- [Stochastic Bandits for Multi-platform Budget Optimization in Online Advertising](https://mlsanity.com/paper/2103.10246/) (2021)
- [Bandits with Partially Observable Confounded Data](https://mlsanity.com/paper/2006.06731/) (2020)
- [Improved High-Probability Regret for Adversarial Bandits with Time-Varying Feedback Graphs](https://mlsanity.com/paper/2210.01376/) (2022)

## Built on by (most cited first, 1 of 1)

- [Efficient and Sharp Off-Policy Learning under Unobserved Confounding](https://mlsanity.com/paper/2502.13022/) (2025)

## Abstract (arXiv)

This paper studies bandit problems where an agent has access to offline data that might be utilized to potentially improve the estimation of each arm's reward distribution. A major obstacle in this setting is the existence of compound biases from the observational data. Ignoring these biases and blindly fitting a model with the biased data could even negatively affect the online learning phase. In this work, we formulate this problem from a causal perspective. First, we categorize the biases into confounding bias and selection bias based on the causal structure they imply. Next, we extract the causal bound for each arm that is robust towards compound biases from biased observational data. The derived bounds contain the ground truth mean reward and can effectively guide the bandit agent to learn a nearly-optimal decision policy. We also conduct regret analysis in both contextual and non-contextual bandit settings and show that prior causal bounds could help consistently reduce the asymptotic regret.