ICML 2025

Multi-Objective Causal Bayesian Optimization
Shriya Bhatija 1 2 Paul-David Zuercher 2 3 Jakob Thumm 1 Thomas Bohn´e 2
Abstract
In decision-making problems, the outcome of
an intervention often depends on the causal
relationships between system components and
is highly costly to evaluate.
In such settings,
causal Bayesian optimization (CBO) exploits the
causal relationships between the system variables
and sequentially performs interventions to ap-
proach the optimum with minimal data. Extend-
ing CBO to the multi-outcome setting, we pro-
pose multi-objective causal Bayesian optimiza-
tion (MO-CBO), a paradigm for identifying Pareto-
optimal interventions within a known multi-target
causal graph.
Our methodology first reduces
the search space by discarding sub-optimal in-
terventions based on the structure of the given
causal graph. We further show that any MO-CBO
problem can be decomposed into several tradi-
tional multi-objective optimization tasks. Our
proposed MO-CBO algorithm is designed to iden-
tify Pareto-optimal interventions by iteratively ex-
ploring these underlying tasks, guided by relative
hypervolume improvement. Experiments on syn-
thetic and real-world causal graphs demonstrate
the superiority of our approach over non-causal
multi-objective Bayesian optimization in settings
where causal information is available.
1. Introduction
Decision-making problems arise in various domains, such
as healthcare, manufacturing, and public policy, and in-
volve manipulating variables to obtain an outcome of in-
terest. In many such domains, interventions are inherently
costly, and practical applications are subject to budgetary
constraints. Moreover, these systems are often governed
1Department of Computer Engineering, Technical University of
Munich, Munich, Germany 2Department of Engineering, Univer-
sity of Cambridge, Cambridge, United Kingdom 3The Alan Turing
Institute, London, United Kingdom. Correspondence to: Shriya
Bhatija <shriya.bhatija@tum.de>.
Proceedings ...