ANACONDA: An Improved Dynamic Regret Algorithm for Adaptive Non-Stationary Dueling Bandits

We study the problem of non-stationary dueling bandits and provide the first adaptive dynamic regret algorithm for this problem. The only two existing attempts in this line of work fall short across multiple dimensions, including pessimistic measures of non-stationary complexity and non-adaptive parameter tuning that requires knowledge of the number of preference changes. We develop an elimination-based rescheduling algorithm to overcome these shortcomings and show a near-optimal $\tilde O(\sqrt{S^{CW} T})$ dynamic regret bound, where $\S^{CW}$ is the number of times the Condorcet winner changes in $T$ rounds. This yields the first near-optimal dynamic regret bound for unknown $S^{CW}$. We further study other related notions of non-stationarity for which we also prove near-optimal dynamic regret guarantees under additional assumptions on the preference model.