PAC-Bayesian Analysis of Contextual Bandits
Yevgeny Seldin, Peter Auer, François Laviolette, John Shawe-Taylor and Ronald Ortner
In: Neural Information Processing Systems, 12-15 Dec 2011, Granada, Spain.

## Abstract

We derive an instantaneous (per-round) data-dependent regret bound for stochastic multiarmed bandits with side information (also known as contextual bandits). The scaling of our regret bound with the number of states (contexts) $N$ goes as $\sqrt{N I_{\rho_t}(S;A)}$, where $I_{\rho_t}(S;A)$ is the mutual information between states and actions (the side information) used by the algorithm at round $t$. If the algorithm uses all the side information, the regret bound scales as $\sqrt{N \ln K}$, where $K$ is the number of actions (arms). However, if the side information $I_{\rho_t}(S;A)$ is not fully used, the regret bound is significantly tighter. In the extreme case, when $I_{\rho_t}(S;A) = 0$, the dependence on the number of states reduces from linear to logarithmic. Our analysis allows to provide the algorithm large amount of side information, let the algorithm to decide which side information is relevant for the task, and penalize the algorithm only for the side information that it is using de facto. We also present an algorithm for multiarmed bandits with side information with $O(K)$ computational complexity per game round.

 PDF - Requires Adobe Acrobat Reader or other PDF viewer.
EPrint Type: Conference or Workshop Item (Paper) Project Keyword UNSPECIFIED Computational, Information-Theoretic Learning with StatisticsLearning/Statistics & OptimisationTheory & AlgorithmsCOMPLACS 8826 Yevgeny Seldin 21 February 2012