Multi-Objective Causal Bayesian Optimization

TL;DR

This work introduces multi-objective causal Bayesian optimization (MO-CBO), a framework for identifying Pareto-optimal interventions in known multi-target causal graphs where evaluations are costly. It decomposes MO-CBO into local MOBO problems and proves that solving a reduced set of possibly Pareto-optimal minimal intervention sets suffices to recover the causal Pareto front, enabling efficient search. The authors propose Causal ParetoSelect, an algorithm that balances exploration across local problems using relative hypervolume improvement, and show it outperforms non-causal MOBO on synthetic and real-world healthcare graphs in terms of front coverage and diversity. The approach advances practical decision-making under causal uncertainty by leveraging graph structure to guide multi-objective optimization with interventions.

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) can exploit the causal relationships between the system variables and sequentially perform interventions to approach the optimum with minimal data. Extending CBO to the multi-outcome setting, we propose Multi-Objective Causal Bayesian Optimization (MO-CBO), a paradigm for identifying Pareto-optimal interventions within a known multi-target causal graph. We first derive a graphical characterization for potentially optimal sets of variables to intervene upon. Showing that any MO-CBO problem can be decomposed into several traditional multi-objective optimization tasks, we then introduce an algorithm that sequentially balances exploration across these tasks using relative hypervolume improvement. The proposed method will be validated on both synthetic and real-world causal graphs, demonstrating its superiority over traditional (non-causal) multi-objective Bayesian optimization in settings where causal information is available.

Figures (12)

• Figure 1: mo-cbo problem in healthcare. (a) Causal graph where red, grey, and orange nodes depict target, manipulative, and non-manipulative variables, respectively. (b) The solution consists of interventions that yield optimal trade-offs between the targets.
• Figure 2: Overview of the mo-cbo methodology.
• Figure 3: Two causal graphs with $\mathbf{X}=\{ X_1,X_2,X_3,X_4\}$, $\mathbf{Y}=\{Y_1,Y_2\}$. (a) No unobserved confounders. (b) An unobserved confounder between $X_4$ and $Y_1$ depicted with the dashed bi-directed edge.
• Figure 4: Convergence to the causal Pareto front across all experiments, measured by the generational distance (upper row) and inverted generational distance (lower row). Lower values indicate better approximations of the ground-truth. The number of interventions refers to the count of intervention variables that were intervened upon. Shaded areas represent $\pm$ standard deviation across 10.0 random seeds.
• Figure 5: synthetic-1. Causal Pareto front approximations. Our method offers a higher coverage of the ground-truth causal Pareto front.

Theorems & Definitions (25)

• Definition 2.1: Pareto optimality
• Definition 3.1: Pareto-optimal intervention set-value pair
• Definition 3.2: Causal Pareto front
• Definition 3.3: Local mo-cbo problem
• Proposition 3.4
• Definition 4.1: Minimal intervention set
• Proposition 4.2
• Definition 4.3: Possibly Pareto-optimal minimal intervention set
• Proposition 4.4
• Definition 4.5: Minimal unobserved confounders' territory