  In this work, we study the performance of the Thompson Sampling algorithm for
Contextual Bandit problems based on the framework introduced by Neu et al. and
their concept of lifted information ratio. First, we prove a comprehensive
bound on the Thompson Sampling expected cumulative regret that depends on the
mutual information of the environment parameters and the history. Then, we
introduce new bounds on the lifted information ratio that hold for sub-Gaussian
rewards, thus generalizing the results from Neu et al. which analysis requires
binary rewards. Finally, we provide explicit regret bounds for the special
cases of unstructured bounded contextual bandits, structured bounded contextual
bandits with Laplace likelihood, structured Bernoulli bandits, and bounded
linear contextual bandits.
