Neural Variance-aware Dueling Bandits with Deep Representation and Shallow Exploration (2506.01250v1)

Abstract: In this paper, we address the contextual dueling bandit problem by proposing variance-aware algorithms that leverage neural networks to approximate nonlinear utility functions. Our approach employs a \textit{variance-aware exploration strategy}, which adaptively accounts for uncertainty in pairwise comparisons while relying only on the gradients with respect to the learnable parameters of the last layer. This design effectively balances the exploration--exploitation tradeoff under both the Upper Confidence Bound (UCB) and Thompson Sampling (TS) frameworks. As a result, under standard assumptions, we establish theoretical guarantees showing that our algorithms achieve sublinear cumulative average regret of order $\bigol\lt(d \sqrt{\sum_{t=1}^T \sigma_t^2} + \sqrt{dT}\rt),$ for sufficiently wide neural networks, where $ d $ is the contextual dimension, $ \sigma_t^2 $ the variance of comparisons at round $ t $, and $ T $ the total number of rounds. We also empirically validate that our approach offers reasonable computational efficiency and achieves sublinear regret on both synthetic tasks with nonlinear utilities and real-world tasks, outperforming existing methods.