Adversarial Causal Bayesian Optimization

TL;DR

This paper introduces Adversarial Causal Bayesian Optimization (ACBO), a framework that accounts for external interventions and adversarial influences, with an algorithm that adapts to non-stationary environments using causal modeling and online learning.

Contribution

It formalizes ACBO, develops the first bounded regret algorithm CBO-MW, and demonstrates scalability and effectiveness in synthetic and real-world scenarios.

Findings

CBO-MW outperforms non-causal methods in experiments.

The approach effectively models external interventions.

Regret bounds depend on causal graph properties.

Abstract

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.