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Structured Linear Contextual Bandits: A Sharp and Geometric Smoothed Analysis
Vidyashankar Sivakumar · Steven Wu · Arindam Banerjee

Wed Jul 15 08:00 AM -- 08:45 AM & Wed Jul 15 09:00 PM -- 09:45 PM (PDT) @ None #None
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.

Author Information

Vidyashankar Sivakumar (Walmart Labs)
Steven Wu (University of Minnesota)
Arindam Banerjee (University of Minnesota)

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