Neural Variance-aware Dueling Bandits with Deep Representation and Shallow Exploration

TL;DR

This paper introduces variance-aware neural algorithms for the contextual dueling bandit problem, balancing exploration and exploitation with theoretical guarantees and empirical validation.

Contribution

It proposes a novel variance-aware exploration strategy using neural networks, providing the first theoretical regret bounds for this setting.

Findings

Achieves sublinear regret in synthetic and real-world tasks.

Balances exploration and exploitation effectively under UCB and TS frameworks.

Outperforms existing methods in empirical evaluations.

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.