# Improved Bound for Robust Causal Bandits with Linear Models

arXiv: https://arxiv.org/abs/2405.07795 · HTML: https://mlsanity.com/paper/2405.07795/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 39 references that are in the map.
- First posted on arXiv 13 May 2024.

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

- [Learning with Good Feature Representations in Bandits and in RL with a Generative Model](https://mlsanity.com/paper/1911.07676/) (2019)
- [Causal Bandits: Learning Good Interventions via Causal Inference](https://mlsanity.com/paper/1606.03203/) (2016)
- [Weighted Linear Bandits for Non-Stationary Environments](https://mlsanity.com/paper/1909.09146/) (2019)
- [Adapting to Misspecification in Contextual Bandits](https://mlsanity.com/paper/2107.05745/) (2021)
- [Stochastic Linear Bandits Robust to Adversarial Attacks](https://mlsanity.com/paper/2007.03285/) (2020)
- [Nearly Optimal Algorithms for Linear Contextual Bandits with Adversarial Corruptions](https://mlsanity.com/paper/2205.06811/) (2022)
- [Achieving Near Instance-Optimality and Minimax-Optimality in Stochastic and Adversarial Linear Bandits Simultaneously](https://mlsanity.com/paper/2102.05858/) (2021)
- [Causal Discovery in the Presence of Missing Data](https://mlsanity.com/paper/1807.04010/) (2018)
- [A Model Selection Approach for Corruption Robust Reinforcement Learning](https://mlsanity.com/paper/2110.03580/) (2021)
- [Learning Graph-Level Representation for Drug Discovery](https://mlsanity.com/paper/1709.03741/) (2017)
- [Misspecified Linear Bandits](https://mlsanity.com/paper/1704.06880/) (2017)
- [Identifying Best Interventions through Online Importance Sampling](https://mlsanity.com/paper/1701.02789/) (2017)
- [Budgeted and Non-budgeted Causal Bandits](https://mlsanity.com/paper/2012.07058/) (2020)
- [Causal Bandits with Unknown Graph Structure](https://mlsanity.com/paper/2106.02988/) (2021)
- [Model-based Causal Bayesian Optimization](https://mlsanity.com/paper/2211.10257/) (2022)
- [Stochastic Linear Optimization with Adversarial Corruption](https://mlsanity.com/paper/1909.02109/) (2019)
- [Causal Bandits with Propagating Inference](https://mlsanity.com/paper/1806.02252/) (2018)
- [Adapting to Misspecification in Contextual Bandits with Offline Regression Oracles](https://mlsanity.com/paper/2102.13240/) (2021)
- [Linear Contextual Bandits with Adversarial Corruptions](https://mlsanity.com/paper/2110.12615/) (2021)
- [Causal Bandits for Linear Structural Equation Models](https://mlsanity.com/paper/2208.12764/) (2022)
- [Adaptively Exploiting d-Separators with Causal Bandits](https://mlsanity.com/paper/2202.05100/) (2022)
- [Causal Bandits without prior knowledge using separating sets](https://mlsanity.com/paper/2009.07916/) (2020)
- [Combinatorial Causal Bandits](https://mlsanity.com/paper/2206.01995/) (2022)
- [A Causal Bandit Approach to Learning Good Atomic Interventions in Presence of Unobserved Confounders](https://mlsanity.com/paper/2107.02772/) (2021)
- [Causal Bandits without Graph Learning](https://mlsanity.com/paper/2301.11401/) (2023)
- [Additive Causal Bandits with Unknown Graph](https://mlsanity.com/paper/2306.07858/) (2023)
- [Causal Discovery in the Presence of Measurement Error: Identifiability Conditions](https://mlsanity.com/paper/1706.03768/) (2017)
- [Combinatorial Causal Bandits without Graph Skeleton](https://mlsanity.com/paper/2301.13392/) (2023)
- [Learning Good Interventions in Causal Graphs via Covering](https://mlsanity.com/paper/2305.04638/) (2023)
- [Robust Causal Bandits for Linear Models](https://mlsanity.com/paper/2310.19794/) (2023)

## Built on by (most cited first, 2 of 2)

- [Linear Causal Bandits: Unknown Graph and Soft Interventions](https://mlsanity.com/paper/2411.02383/) (2024)
- [Evaluating and Learning Robust Bandit Policies Under Uncertain Causal Mechanisms](https://mlsanity.com/paper/2508.02812/) (2025)

## Abstract (arXiv)

This paper investigates the robustness of causal bandits (CBs) in the face of temporal model fluctuations. This setting deviates from the existing literature's widely-adopted assumption of constant causal models. The focus is on causal systems with linear structural equation models (SEMs). The SEMs and the time-varying pre- and post-interventional statistical models are all unknown and subject to variations over time. The goal is to design a sequence of interventions that incur the smallest cumulative regret compared to an oracle aware of the entire causal model and its fluctuations. A robust CB algorithm is proposed, and its cumulative regret is analyzed by establishing both upper and lower bounds on the regret. It is shown that in a graph with maximum in-degree d, length of the largest causal path L, and an aggregate model deviation C, the regret is upper bounded by tildeO(d^L-frac12(√T + C)) and lower bounded by Omega(d^fracL2-2max√T; ,; d2C). The proposed algorithm achieves nearly optimal tildeO(√T) regret when C is o(√T), maintaining sub-linear regret for a broad range of C.