# Causal Bandits with General Causal Models and Interventions

arXiv: https://arxiv.org/abs/2403.00233 · HTML: https://mlsanity.com/paper/2403.00233/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 46 references that are in the map.
- First posted on arXiv 1 Mar 2024.

## Builds on (most cited first, 21 of 21)

- [Model-based Reinforcement Learning and the Eluder Dimension](https://mlsanity.com/paper/1406.1853/) (2014)
- [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)
- [Randomized Exploration in Generalized Linear Bandits](https://mlsanity.com/paper/1906.08947/) (2019)
- [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)
- [Causal Bandits with Propagating Inference](https://mlsanity.com/paper/1806.02252/) (2018)
- [Understanding the Eluder Dimension](https://mlsanity.com/paper/2104.06970/) (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)
- [Combinatorial Pure Exploration of Causal Bandits](https://mlsanity.com/paper/2206.07883/) (2022)
- [A Short Note on the Relationship of Information Gain and Eluder Dimension](https://mlsanity.com/paper/2107.02377/) (2021)
- [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)

## Built on by (most cited first, 7 of 7)

- [Linear Causal Bandits: Unknown Graph and Soft Interventions](https://mlsanity.com/paper/2411.02383/) (2024)
- [Reinforcement Learning in the Real World: A Survey of Statistical Challenges and Future Directions](https://mlsanity.com/paper/2601.15353/) (2026)
- [Transfer Learning in Latent Contextual Bandits with Covariate Shift Through Causal Transportability](https://mlsanity.com/paper/2502.20153/) (2025)
- [Asymmetric Graph Error Control with Low Complexity in Causal Bandits](https://mlsanity.com/paper/2408.11240/) (2024)
- [Causal Contextual Bandits with Adaptive Context](https://mlsanity.com/paper/2405.18626/) (2024)
- [ModalImmune: Immunity Driven Unlearning via Self Destructive Training](https://mlsanity.com/paper/2602.16197/) (2026)
- [Graph Structured Combinatorial Semi-Bandit with Nonlinear Reward Associations through Separable Signals](https://mlsanity.com/paper/2606.14650/) (2026)

## Abstract (arXiv)

This paper considers causal bandits (CBs) for the sequential design of interventions in a causal system. The objective is to optimize a reward function via minimizing a measure of cumulative regret with respect to the best sequence of interventions in hindsight. The paper advances the results on CBs in three directions. First, the structural causal models (SCMs) are assumed to be unknown and drawn arbitrarily from a general class F of Lipschitz-continuous functions. Existing results are often focused on (generalized) linear SCMs. Second, the interventions are assumed to be generalized soft with any desired level of granularity, resulting in an infinite number of possible interventions. The existing literature, in contrast, generally adopts atomic and hard interventions. Third, we provide general upper and lower bounds on regret. The upper bounds subsume (and improve) known bounds for special cases. The lower bounds are generally hitherto unknown. These bounds are characterized as functions of the (i) graph parameters, (ii) eluder dimension of the space of SCMs, denoted by operatornamedim(F), and (iii) the covering number of the function space, denoted by rm cn(F). Specifically, the cumulative achievable regret over horizon T is O(K dL-1√Toperatornamedim(F) log(rm cn(F))), where K is related to the Lipschitz constants, d is the graph's maximum in-degree, and L is the length of the longest causal path. The upper bound is further refined for special classes of SCMs (neural network, polynomial, and linear), and their corresponding lower bounds are provided.