Optimal and Adaptive Non-Stationary Dueling Bandits Under a Generalized Borda Criterion

In dueling bandits, the learner receives preference feedback between arms, and the regret of an arm is defined in terms of its suboptimality to a winner arm. The more challenging and practically motivated non-stationary variant of dueling bandits, where preferences change over time, has been the focus of several recent works (Saha and Gupta, 2022; Buening and Saha, 2023; Suk and Agarwal, 2023). The goal is to design algorithms without foreknowledge of the amount of change. The bulk of known results here studies the Condorcet winner setting, where an arm preferred over any other exists at all times. Yet, such a winner may not exist and, to contrast, the Borda version of this problem (which is always well-defined) has received little attention. In this work, we establish the first optimal and adaptive Borda dynamic regret upper bound, which highlights fundamental differences in the learnability of severe non-stationarity between Condorcet vs. Borda regret objectives in dueling bandits. Surprisingly, our techniques for non-stationary Borda dueling bandits also yield improved rates within the Condorcet winner setting, and reveal new preference models where tighter notions of non-stationarity are adaptively learnable. This is accomplished through a novel generalized Borda score framework which unites the Borda and Condorcet problems, thus allowing reduction of Condorcet regret to a Borda-like task. Such a generalization was not previously known and is likely to be of independent interest.