# Adversarial Causal Bayesian Optimization

arXiv: https://arxiv.org/abs/2307.16625 · HTML: https://mlsanity.com/paper/2307.16625/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 30 references that are in the map.
- First posted on arXiv 31 Jul 2023.

## Builds on (most cited first, 17 of 17)

- [Efficient Model-Based Reinforcement Learning through Optimistic Policy Search and Planning](https://mlsanity.com/paper/2006.08684/) (2020)
- [Adversarially Robust Optimization with Gaussian Processes](https://mlsanity.com/paper/1810.10775/) (2018)
- [Distributionally Robust Bayesian Optimization](https://mlsanity.com/paper/2002.09038/) (2020)
- [Causal Bayesian Optimization](https://mlsanity.com/paper/2005.11741/) (2020)
- [Bayesian Optimization of Function Networks](https://mlsanity.com/paper/2112.15311/) (2021)
- [Model-based Causal Bayesian Optimization](https://mlsanity.com/paper/2211.10257/) (2022)
- [Submodular Functions: from Discrete to Continous Domains](https://mlsanity.com/paper/1511.00394/) (2015)
- [Continuous DR-submodular Maximization: Structure and Algorithms](https://mlsanity.com/paper/1711.02515/) (2017)
- [No-Regret Learning in Unknown Games with Correlated Payoffs](https://mlsanity.com/paper/1909.08540/) (2019)
- [Learning to Play Sequential Games versus Unknown Opponents](https://mlsanity.com/paper/2007.05271/) (2020)
- [Mean-Variance Analysis in Bayesian Optimization under Uncertainty](https://mlsanity.com/paper/2009.08166/) (2020)
- [Dynamic Causal Bayesian Optimization](https://mlsanity.com/paper/2110.13891/) (2021)
- [Risk-averse Heteroscedastic Bayesian Optimization](https://mlsanity.com/paper/2111.03637/) (2021)
- [Matching a Desired Causal State via Shift Interventions](https://mlsanity.com/paper/2107.01850/) (2021)
- [Distributionally Robust Bayesian Quadrature Optimization](https://mlsanity.com/paper/2001.06814/) (2020)
- [Contextual Games: Multi-Agent Learning with Side Information](https://mlsanity.com/paper/2107.06327/) (2021)
- [Mixed Strategies for Robust Optimization of Unknown Objectives](https://mlsanity.com/paper/2002.12613/) (2020)

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

- [Linear Causal Bandits: Unknown Graph and Soft Interventions](https://mlsanity.com/paper/2411.02383/) (2024)
- [Multi-Objective Causal Bayesian Optimization](https://mlsanity.com/paper/2502.14755/) (2025)
- [Causal Bayesian Optimization with Unknown Graphs](https://mlsanity.com/paper/2503.19554/) (2025)
- [Transferring Information Across Interventions in Causal Bayesian Optimization](https://mlsanity.com/paper/2606.01457/) (2026)

## Abstract (arXiv)

In Causal Bayesian Optimization (CBO), an agent intervenes on an unknown structural causal model to maximize a downstream reward variable. In this paper, we consider the generalization where other agents or external events also intervene on the system, which is key for enabling adaptiveness to non-stationarities such as weather changes, market forces, or adversaries. We formalize this generalization of CBO as Adversarial Causal Bayesian Optimization (ACBO) and introduce the first algorithm for ACBO with bounded regret: Causal Bayesian Optimization with Multiplicative Weights (CBO-MW). Our approach combines a classical online learning strategy with causal modeling of the rewards. To achieve this, it computes optimistic counterfactual reward estimates by propagating uncertainty through the causal graph. We derive regret bounds for CBO-MW that naturally depend on graph-related quantities. We further propose a scalable implementation for the case of combinatorial interventions and submodular rewards. Empirically, CBO-MW outperforms non-causal and non-adversarial Bayesian optimization methods on synthetic environments and environments based on real-word data. Our experiments include a realistic demonstration of how CBO-MW can be used to learn users' demand patterns in a shared mobility system and reposition vehicles in strategic areas.