ANACONDA: An Improved Dynamic Regret Algorithm for Adaptive Non-Stationary Dueling Bandits
This provides the first adaptive algorithm for dynamic regret in non-stationary dueling bandits, addressing limitations in existing methods for applications like recommendation systems.
The paper tackles the problem of non-stationary dueling bandits by developing an elimination-based rescheduling algorithm, achieving a near-optimal dynamic regret bound of $ ilde{O}(\sqrt{S^{ exttt{CW}} T})$ without prior knowledge of preference changes.
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 $\tilde{O}(\sqrt{S^{\texttt{CW}} T})$ dynamic regret bound, where $S^{\texttt{CW}}$ is the number of times the Condorcet winner changes in $T$ rounds. This yields the first near-optimal dynamic regret algorithm for unknown $S^{\texttt{CW}}$. We further study other related notions of non-stationarity for which we also prove near-optimal dynamic regret guarantees under additional assumptions on the underlying preference model.