  Computationally efficient contextual bandits are often based on estimating a
predictive model of rewards given contexts and arms using past data. However,
when the reward model is not well-specified, the bandit algorithm may incur
unexpected regret, so recent work has focused on algorithms that are robust to
misspecification. We propose a simple family of contextual bandit algorithms
that adapt to misspecification error by reverting to a good safe policy when
there is evidence that misspecification is causing a regret increase. Our
algorithm requires only an offline regression oracle to ensure regret
guarantees that gracefully degrade in terms of a measure of the average
misspecification level. Compared to prior work, we attain similar regret
guarantees, but we do no rely on a master algorithm, and do not require more
robust oracles like online or constrained regression oracles (e.g., Foster et
al. (2020a); Krishnamurthy et al. (2020)). This allows us to design algorithms
for more general function approximation classes.
