Optimal Observation-Intervention Trade-Off in Optimisation Problems with Causal Structure

TL;DR

This paper introduces a non-myopic approach to optimize expensive functions with causal structure knowledge, balancing observation and intervention to improve efficiency in Bayesian optimization.

Contribution

It formulates the observation-intervention trade-off as an optimal stopping problem and integrates it with existing causal Bayesian optimization methods.

Findings

Enhanced optimization efficiency on real and synthetic benchmarks.

Theoretical characterization of optimal stopping times.

Improved performance over traditional methods ignoring causal structure.

Abstract

We consider the problem of optimising an expensive-to-evaluate grey-box objective function, within a finite budget, where known side-information exists in the form of the causal structure between the design variables. Standard black-box optimisation ignores the causal structure, often making it inefficient and expensive. The few existing methods that consider the causal structure are myopic and do not fully accommodate the observation-intervention trade-off that emerges when estimating causal effects. In this paper, we show that the observation-intervention trade-off can be formulated as a non-myopic optimal stopping problem which permits an efficient solution. We give theoretical results detailing the structure of the optimal stopping times and demonstrate the generality of our approach by showing that it can be integrated with existing causal Bayesian optimisation algorithms. Experimental results show that our formulation can enhance existing algorithms on real and synthetic benchmarks.