# Robust Causal Bandits for Linear Models

arXiv: https://arxiv.org/abs/2310.19794 · HTML: https://mlsanity.com/paper/2310.19794/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 39 references that are in the map.
- First posted on arXiv 30 Oct 2023.

## Builds on (most cited first, 28 of 28)

- [Learning with Good Feature Representations in Bandits and in RL with a Generative Model](https://mlsanity.com/paper/1911.07676/) (2019)
- [CausalWorld: A Robotic Manipulation Benchmark for Causal Structure and Transfer Learning](https://mlsanity.com/paper/2010.04296/) (2020)
- [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)
- [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)
- [Robust Stochastic Linear Contextual Bandits Under Adversarial Attacks](https://mlsanity.com/paper/2106.02978/) (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)
- [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)
- [Matching a Desired Causal State via Shift Interventions](https://mlsanity.com/paper/2107.01850/) (2021)
- [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)
- [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)

## Built on by (most cited first, 4 of 4)

- [Linear Causal Bandits: Unknown Graph and Soft Interventions](https://mlsanity.com/paper/2411.02383/) (2024)
- [Improved Bound for Robust Causal Bandits with Linear Models](https://mlsanity.com/paper/2405.07795/) (2024)
- [Asymmetric Graph Error Control with Low Complexity in Causal Bandits](https://mlsanity.com/paper/2408.11240/) (2024)
- [Evaluating and Learning Robust Bandit Policies Under Uncertain Causal Mechanisms](https://mlsanity.com/paper/2508.02812/) (2025)

## Abstract (arXiv)

Sequential design of experiments for optimizing a reward function in causal systems can be effectively modeled by the sequential design of interventions in causal bandits (CBs). In the existing literature on CBs, a critical assumption is that the causal models remain constant over time. However, this assumption does not necessarily hold in complex systems, which constantly undergo temporal model fluctuations. This paper addresses the robustness of CBs to such model fluctuations. 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. Cumulative regret is adopted as the design criteria, based on which the objective is to design a sequence of interventions that incur the smallest cumulative regret with respect to an oracle aware of the entire causal model and its fluctuations. First, it is established that the existing approaches fail to maintain regret sub-linearity with even a few instances of model deviation. Specifically, when the number of instances with model deviation is as few as T^frac12L, where T is the time horizon and L is the longest causal path in the graph, the existing algorithms will have linear regret in T. Next, a robust CB algorithm is designed, and its regret is analyzed, where upper and information-theoretic lower bounds on the regret are established. Specifically, in a graph with N nodes and maximum degree d, under a general measure of model deviation C, the cumulative regret is upper bounded by tildeO(d^L-frac12(√NT + NC)) and lower bounded by Omega(d^fracL2-2max√T,d2C). Comparing these bounds establishes that the proposed algorithm achieves nearly optimal tildeO(√T) regret when C is o(√T) and maintains sub-linear regret for a broader range of C.