  A major research direction in contextual bandits is to develop algorithms
that are computationally efficient, yet support flexible, general-purpose
function approximation. Algorithms based on modeling rewards have shown strong
empirical performance, but typically require a well-specified model, and can
fail when this assumption does not hold. Can we design algorithms that are
efficient and flexible, yet degrade gracefully in the face of model
misspecification? We introduce a new family of oracle-efficient algorithms for
$\varepsilon$-misspecified contextual bandits that adapt to unknown model
misspecification -- both for finite and infinite action settings. Given access
to an online oracle for square loss regression, our algorithm attains optimal
regret and -- in particular -- optimal dependence on the misspecification
level, with no prior knowledge. Specializing to linear contextual bandits with
infinite actions in $d$ dimensions, we obtain the first algorithm that achieves
the optimal $O(d\sqrt{T} + \varepsilon\sqrt{d}T)$ regret bound for unknown
misspecification level $\varepsilon$.
  On a conceptual level, our results are enabled by a new optimization-based
perspective on the regression oracle reduction framework of Foster and Rakhlin,
which we anticipate will find broader use.
