  Bandit learning algorithms typically involve the balance of exploration and
exploitation. However, in many practical applications, worst-case scenarios
needing systematic exploration are seldom encountered. In this work, we
consider a smoothed setting for structured linear contextual bandits where the
adversarial contexts are perturbed by Gaussian noise and the unknown parameter
$\theta^*$ has structure, e.g., sparsity, group sparsity, low rank, etc. We
propose simple greedy algorithms for both the single- and multi-parameter
(i.e., different parameter for each context) settings and provide a unified
regret analysis for $\theta^*$ with any assumed structure. The regret bounds
are expressed in terms of geometric quantities such as Gaussian widths
associated with the structure of $\theta^*$. We also obtain sharper regret
bounds compared to earlier work for the unstructured $\theta^*$ setting as a
consequence of our improved analysis. We show there is implicit exploration in
the smoothed setting where a simple greedy algorithm works.
