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PAC-Bayesian Analysis of Contextual Bandits
Yevgeny Seldin · Peter Auer · Francois Laviolette · John Shawe-Taylor · Ronald Ortner

Tue Dec 13 08:45 AM -- 02:59 PM (PST) @
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 computational complexity that is a linear in the number of actions.

Author Information

Yevgeny Seldin (University of Copenhagen)
Peter Auer (Montanuniversitaet Leoben)
Francois Laviolette (Université Laval)
John Shawe-Taylor (UCL)

John Shawe-Taylor has contributed to fields ranging from graph theory through cryptography to statistical learning theory and its applications. However, his main contributions have been in the development of the analysis and subsequent algorithmic definition of principled machine learning algorithms founded in statistical learning theory. This work has helped to drive a fundamental rebirth in the field of machine learning with the introduction of kernel methods and support vector machines, driving the mapping of these approaches onto novel domains including work in computer vision, document classification, and applications in biology and medicine focussed on brain scan, immunity and proteome analysis. He has published over 300 papers and two books that have together attracted over 60000 citations. He has also been instrumental in assembling a series of influential European Networks of Excellence. The scientific coordination of these projects has influenced a generation of researchers and promoted the widespread uptake of machine learning in both science and industry that we are currently witnessing.

Ronald Ortner (Montanuniversitaet Leoben)

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