KLUCB Approach to Copeland Bandits

Multi-armed bandit(MAB) problem is a reinforcement learning framework where an agent tries to maximise her profit by proper selection of actions through absolute feedback for each action. The dueling bandits problem is a variation of MAB problem in which an agent chooses a pair of actions and receives relative feedback for the chosen action pair. The dueling bandits problem is well suited for modelling a setting in which it is not possible to provide quantitative feedback for each action, but qualitative feedback for each action is preferred as in the case of human feedback. The dueling bandits have been successfully applied in applications such as online rank elicitation, information retrieval, search engine improvement and clinical online recommendation. We propose a new method called Sup-KLUCB for K-armed dueling bandit problem specifically Copeland bandit problem by converting it into a standard MAB problem. Instead of using MAB algorithm independently for each action in a pair as in Sparring and in Self-Sparring algorithms, we combine a pair of action and use it as one action. Previous UCB algorithms such as Relative Upper Confidence Bound(RUCB) can be applied only in case of Condorcet dueling bandits, whereas this algorithm applies to general Copeland dueling bandits, including Condorcet dueling bandits as a special case. Our empirical results outperform state of the art Double Thompson Sampling(DTS) in case of Copeland dueling bandits.