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

• URL: http://arxiv.org/abs/2411.05979v1
• Date: Fri, 08 Nov 2024 21:24:14 GMT
• Title: Variance-Aware Linear UCB with Deep Representation for Neural Contextual Bandits
• Authors: Ha Manh Bui, Enrique Mallada, Anqi Liu,
• Abstract summary: A neural upper confidence bound (UCB) algorithm has shown success in contextual bandits. We propose a variance-aware algorithm that utilizes $sigma2_t$, i.e., an upper bound of the reward noise variance at round $t$. We provide an oracle version for our algorithm characterized by an oracle variance upper bound $sigma2_t$ and a practical version with a novel estimation for this variance bound.
• Score: 9.877915844066338
• License:
• 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.

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