ArXiv Preprint
How should we intervene on an unknown structural causal model to maximize a
downstream variable of interest? This optimization of the output of a system of
interconnected variables, also known as causal Bayesian optimization (CBO), has
important applications in medicine, ecology, and manufacturing. Standard
Bayesian optimization algorithms fail to effectively leverage the underlying
causal structure. Existing CBO approaches assume noiseless measurements and do
not come with guarantees. We propose model-based causal Bayesian optimization
(MCBO), an algorithm that learns a full system model instead of only modeling
intervention-reward pairs. MCBO propagates epistemic uncertainty about the
causal mechanisms through the graph and trades off exploration and exploitation
via the optimism principle. We bound its cumulative regret, and obtain the
first non-asymptotic bounds for CBO. Unlike in standard Bayesian optimization,
our acquisition function cannot be evaluated in closed form, so we show how the
reparameterization trick can be used to apply gradient-based optimizers.
Empirically we find that MCBO compares favorably with existing state-of-the-art
approaches.
Scott Sussex, Anastasiia Makarova, Andreas Krause
2022-11-18
