[2411.05979] Variance-Aware Linear UCB with Deep Representation for Neural Contextual Bandits

View a PDF of the paper titled Variance-Aware Linear UCB with Deep Representation for Neural Contextual Bandits, by Ha Manh Bui and 2 other authors

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Abstract:By leveraging the representation power of deep neural networks, neural upper confidence bound (UCB) algorithms have shown success in contextual bandits. To further balance the exploration and exploitation, we propose Neural-$\sigma^2$-LinearUCB, a variance-aware algorithm that utilizes $\sigma^2_t$, i.e., an upper bound of the reward noise variance at round $t$, to enhance the uncertainty quantification quality of the UCB, resulting in a regret performance improvement. We provide an oracle version for our algorithm characterized by an oracle variance upper bound $\sigma^2_t$ and a practical version with a novel estimation for this variance bound. Theoretically, we provide rigorous regret analysis for both versions and prove that our oracle algorithm achieves a better regret guarantee than other neural-UCB algorithms in the neural contextual bandits setting. Empirically, our practical method enjoys a similar computational efficiency, while outperforming state-of-the-art techniques by having a better calibration and lower regret across multiple standard settings, including on the synthetic, UCI, MNIST, and CIFAR-10 datasets.