  We consider Bayesian optimization in settings where observations can be
adversarially biased, for example by an uncontrolled hidden confounder. Our
first contribution is a reduction of the confounded setting to the dueling
bandit model. Then we propose a novel approach for dueling bandits based on
information-directed sampling (IDS). Thereby, we obtain the first efficient
kernelized algorithm for dueling bandits that comes with cumulative regret
guarantees. Our analysis further generalizes a previously proposed
semi-parametric linear bandit model to non-linear reward functions, and
uncovers interesting links to doubly-robust estimation.
