Copeland Dueling Bandits
This work addresses a key limitation in dueling bandits for decision-making systems, offering a scalable solution with theoretical guarantees, though it is incremental in improving regret bounds.
The paper tackles the dueling bandit problem when a Condorcet winner may not exist by proposing two algorithms, CCB and SCB, that minimize regret with respect to the Copeland winner, achieving O(K log T) regret bounds without restrictive assumptions, improving over prior results that required O(K^2 log T) or restrictive assumptions.
A version of the dueling bandit problem is addressed in which a Condorcet winner may not exist. Two algorithms are proposed that instead seek to minimize regret with respect to the Copeland winner, which, unlike the Condorcet winner, is guaranteed to exist. The first, Copeland Confidence Bound (CCB), is designed for small numbers of arms, while the second, Scalable Copeland Bandits (SCB), works better for large-scale problems. We provide theoretical results bounding the regret accumulated by CCB and SCB, both substantially improving existing results. Such existing results either offer bounds of the form $O(K \log T)$ but require restrictive assumptions, or offer bounds of the form $O(K^2 \log T)$ without requiring such assumptions. Our results offer the best of both worlds: $O(K \log T)$ bounds without restrictive assumptions.