Efficient and Optimal Algorithms for Contextual Dueling Bandits under Realizability
This provides an efficient solution for sequential decision-making with preference feedback, addressing a specific bottleneck in bandit algorithms.
The paper tackles the contextual dueling bandit problem under realizability by introducing a new algorithm that achieves the optimal regret rate for a stronger performance measure, resolving an open problem from prior work.
We study the $K$-armed contextual dueling bandit problem, a sequential decision making setting in which the learner uses contextual information to make two decisions, but only observes \emph{preference-based feedback} suggesting that one decision was better than the other. We focus on the regret minimization problem under realizability, where the feedback is generated by a pairwise preference matrix that is well-specified by a given function class $\mathcal F$. We provide a new algorithm that achieves the optimal regret rate for a new notion of best response regret, which is a strictly stronger performance measure than those considered in prior works. The algorithm is also computationally efficient, running in polynomial time assuming access to an online oracle for square loss regression over $\mathcal F$. This resolves an open problem of Dudík et al. [2015] on oracle efficient, regret-optimal algorithms for contextual dueling bandits.