PAC-Bayesian analysis of contextual bandits

TY - GEN

T1 - PAC-Bayesian analysis of contextual bandits

AU - Seldin, Yevgeny

AU - Auer, Peter

AU - Laviolette, François

AU - Shawe-Taylor, John

AU - Ortner, Ronald

PY - 2011

Y1 - 2011

N2 - We derive an instantaneous (per-round) data-dependent regret bound for stochastic multiarmed bandits with side information (also known as contextual bandits). pThe scaling of our regret bound with the number of states (contexts) N goes as √NI pt (S;A), where I pt (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 √N lnK, where K is the number of actions (arms). However, if the side information I pt (S;A) is not fully used, the regret bound is significantly tighter. In the extreme case, when I pt (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.

AB - We derive an instantaneous (per-round) data-dependent regret bound for stochastic multiarmed bandits with side information (also known as contextual bandits). pThe scaling of our regret bound with the number of states (contexts) N goes as √NI pt (S;A), where I pt (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 √N lnK, where K is the number of actions (arms). However, if the side information I pt (S;A) is not fully used, the regret bound is significantly tighter. In the extreme case, when I pt (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.

M3 - Article in proceedings

BT - Advances in Neural Information Processing Systems (NIPS)

ER -