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The contextual bandit problem is a theoretically justified framework withwide applications in various fields. While the previous study on this problemusually requires independence between noise and contexts, our work considers amore sensible setting where the noise becomes a latent confounder that affectsboth contexts and rewards. Such a confounded setting is more realistic andcould expand to a broader range of applications. However, the unresolvedconfounder will cause a bias in reward function estimation and thus lead to alarge regret. To deal with the challenges brought by the confounder, we applythe dual instrumental variable regression, which can correctly identify thetrue reward function. We prove the convergence rate of this method isnear-optimal in two types of widely used reproducing kernel Hilbert spaces.Therefore, we can design computationally efficient and regret-optimalalgorithms based on the theoretical guarantees for confounded bandit problems.The numerical results illustrate the efficacy of our proposed algorithms in theconfounded bandit setting.

Dual Instrumental Method for Confounded Kernelized Bandits