Abstract: We investigate the misspecified linear contextual bandit (MLCB) problem, which is a generalization of the linear contextual bandit (LCB) problem. The MLCB problem is a decision-making problem in which a learner observes d-dimensional feature vectors, called arms, chooses an arm from K arms, and then obtains a reward from the chosen arm in each round. The learner aims to maximize the sum of the rewards over T rounds. In contrast to the LCB problem, the rewards in the MLCB problem may not be represented by a linear function in feature vectors; instead, it is approximated by a linear function with additive approximation parameter \varepsilon \geq 0. In this paper, we propose an algorithm that achieves \tilde{O}(\sqrt{dT\log(K)} + \varepsilon\sqrt{d}T) regret, where \tilde{O}(\cdot) ignores polylogarithmic factors in d and T. This is the first algorithm that guarantees a high-probability regret bound for the MLCB problem without knowledge of the approximation parameter \varepsilon.